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On rationally integrable planar dual multibilliards and piecewise smooth projective billiards Nonlinearity (IF 1.7) Pub Date : 2024-04-17 Alexey Glutsyuk
The billiard flow in a planar domain Ω acts on the tangent bundle TR2|Ω as geodesic flow with reflections from the boundary. It has the trivial first integral: squared modulus of the velocity. Bolotin’s conjecture, now a joint theorem of Bialy, Mironov and the author, deals with those billiards whose flow admits an additional integral that is polynomial in the velocity and whose restriction to the
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Average shadowing revisited Nonlinearity (IF 1.7) Pub Date : 2024-04-17 Michael Blank
We propose a novel unifying approach to study the shadowing property for a broad class of dynamical systems (in particular, discontinuous and non-invertible) under a variety of perturbations. In distinction to known constructions, our approach is local: it is based on the gluing property which takes into account the shadowing under a single (not necessarily small) perturbation.
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Entropic transfer operators Nonlinearity (IF 1.7) Pub Date : 2024-04-16 Oliver Junge, Daniel Matthes, Bernhard Schmitzer
We propose a new concept for the regularization and discretization of transfer and Koopman operators in dynamical systems. Our approach is based on the entropically regularized optimal transport between two probability measures. In particular, we use optimal transport plans in order to construct a finite-dimensional approximation of some transfer or Koopman operator which can be analyzed computationally
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Asymptotically quasiperiodic solutions for time-dependent Hamiltonians Nonlinearity (IF 1.7) Pub Date : 2024-04-16 Donato Scarcella
Dynamical systems subject to perturbations that decay over time are relevant in describing many physical models, e.g. when considering the effect of a laser pulse on a molecule, in epidemiological studies, and celestial mechanics. For this purpose, we consider time-dependent Hamiltonian vector fields that are the sum of two components. The first has an invariant torus supporting quasiperiodic solutions
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A mathematical analysis of the adiabatic Dyson equation from time-dependent density functional theory Nonlinearity (IF 1.7) Pub Date : 2024-04-15 Thiago Carvalho Corso
In this article, we analyse the Dyson equation for the density–density response function (DDRF) that plays a central role in linear response time-dependent density functional theory (LR-TDDFT). First, we present a functional analytic setting that allows for a unified treatment of the Dyson equation with general adiabatic approximations for discrete (finite and infinite) and continuum systems. In this
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Growth of curvature and perimeter of temperature patches in the 2D Boussinesq equations Nonlinearity (IF 1.7) Pub Date : 2024-04-12 Jaemin Park
In this paper, we construct an example of temperature patch solutions for the two-dimensional, incompressible Boussinesq system with kinematic viscosity such that both the curvature and perimeter grow to infinity over time. The presented example consists of two disjoint, simply connected patches. The rates of growth for both curvature and perimeter in this example are at least algebraic.
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Well-posedness for the surface quasi-geostrophic front equation Nonlinearity (IF 1.7) Pub Date : 2024-04-11 Albert Ai, Ovidiu-Neculai Avadanei
We consider the well-posedness of the surface quasi-geostrophic (SQG) front equation. Hunter–Shu–Zhang (2021 Pure Appl. Anal. 3 403–72) established well-posedness under a small data condition as well as a convergence condition on an expansion of the equation’s nonlinearity. In the present article, we establish unconditional large data local well-posedness of the SQG front equation, while also improving
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The weak mixing property on negatively curved manifolds Nonlinearity (IF 1.7) Pub Date : 2024-04-10 Yves Coudène
Given a complete manifold of negative curvature, we show that weak mixing is a generic property in the set of all probability measures invariant by the geodesic flow, as soon as the flow is topologically weakly mixing in restriction to its non-wandering set.
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Vanishing viscosity limit for incompressible axisymmetric flow in the exterior of a cylinder Nonlinearity (IF 1.7) Pub Date : 2024-04-08 Jitao Liu
In this paper, we study the initial boundary value problem and vanishing viscosity limit for incompressible axisymmetric Navier–Stokes equations with swirls in the exterior of a cylinder under Navier-slip boundary condition. In the first part, we prove the existence of a unique global solution with the axisymmetric initial data u0ν∈Lσ2(Ω) and axisymmetric force f∈L2([0,T];L2(Ω)) . This result improves
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Geodesic flows of compact higher genus surfaces without conjugate points have expansive factors Nonlinearity (IF 1.7) Pub Date : 2024-04-05 Edhin Franklin Mamani
In this paper we show that a geodesic flow of a compact surface without conjugate points of genus greater than one is time-preserving semi-conjugate to a continuous expansive flow which is topologically mixing and has a local product structure. As an application we show that the geodesic flow of a compact surface without conjugate points of genus greater than one has a unique measure of maximal entropy
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An existence theory for superposition operators of mixed order subject to jumping nonlinearities Nonlinearity (IF 1.7) Pub Date : 2024-04-04 Serena Dipierro, Kanishka Perera, Caterina Sportelli, Enrico Valdinoci
We consider a superposition operator of the form ∫[0,1](−Δ)sudμ(s), for a signed measure µ on the interval of fractional exponents [0,1] , joined to a nonlinearity whose term of homogeneity equal to one is ‘jumping’, i.e. it may present different coefficients in front of the negative and positive parts. The signed measure is supposed to possess a positive contribution coming from the higher exponents
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Weakened vortex stretching effect in three scale hierarchy for the 3D Euler equations Nonlinearity (IF 1.7) Pub Date : 2024-04-03 In-Jee Jeong, Jungkyoung Na, Tsuyoshi Yoneda
We consider the three-dimensional incompressible Euler equations under the following three scale hierarchical situation: large-scale vortex stretching the middle-scale, and at the same time, the middle-scale stretching the small-scale. In this situation, we show that, the stretching effect of this middle-scale flow is weakened by the large-scale. In other words, the vortices being stretched could have
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Invariant measures for random piecewise convex maps Nonlinearity (IF 1.7) Pub Date : 2024-04-03 Tomoki Inoue, Hisayoshi Toyokawa
We establish the existence of Lebesgue-equivalent conservative and ergodic σ -finite invariant measures for a wide class of one-dimensional random maps consisting of piecewise convex maps. We also estimate the size of invariant measures around a small neighbourhood of a fixed point where the invariant density functions may diverge. Application covers random intermittent maps with critical points or
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Spectrality of a class of infinite convolutions on R * Nonlinearity (IF 1.7) Pub Date : 2024-04-03 Sha Wu, Yingqing Xiao
Given an integer m⩾1 . Let Σ(m)={1,2,…,m}N be a symbolic space, and let {(bk,Dk)}k=1m:={(bk,{0,1,…,pk−1}tk)}k=1m be a finite sequence pairs, where integers |bk| , pk⩾2 , |tk|⩾1 and pk,t1,t2,…,tm are pairwise coprime integers for all 1⩽k⩽m . In this paper, we show that for any infinite word σ=(σn)n=1∞∈Σ(m) , the infinite convolution μσ=δbσ1−1Dσ1∗δ(bσ1bσ2)−1Dσ2∗δ(bσ1bσ2bσ3)−1Dσ3∗⋯ is a spectral measure
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Sign-changing bubble tower solutions for a Paneitz-type problem Nonlinearity (IF 1.7) Pub Date : 2024-04-03 Wenjing Chen, Xiaomeng Huang
This paper is concerned with the following biharmonic problem {Δ2u=|u|8N−4uin Ω∖B(ξ0,ε)―,u=Δu=0on ∂(Ω∖B(ξ0,ε)―), where Ω is an open bounded domain in RN , N⩾5 , and B(ξ0,ε) is a ball centered at ξ 0 with radius ɛ, ɛ is a small positive parameter. We obtain the existence of solutions for problem (0.1), which is an arbitrary large number of sign-changing solutions whose profile is a superposition of
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Uniqueness of Denjoy minimal sets for twist maps with zero entropy * Nonlinearity (IF 1.7) Pub Date : 2024-04-02 Zi-Hao Yu, Bai-Nian Shen, Wen-Xin Qin
For monotone twist maps with zero topological entropy, we show that the set of recurrent points with irrational rotation number α can be described by a single orientation preserving circle homeomorphism and hence there is either an invariant circle, or a unique Denjoy minimal set, of rotation number α.
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Hausdorff dimension of recurrence sets Nonlinearity (IF 1.7) Pub Date : 2024-04-02 Zhang-nan Hu, Tomas Persson
We consider linear mappings on the 2-dimensional torus, defined by T(x)=Ax (mod 1) , where A is an invertible 2×2 integer matrix, with no eigenvalues on the unit circle. In the case detA=±1 , we give a formula for the Hausdorff dimension of the set {x∈T2:d(Tn(x),x)
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Long time asymptotics of large data in the Kadomtsev–Petviashvili models Nonlinearity (IF 1.7) Pub Date : 2024-04-02 Argenis J Mendez, Claudio Muñoz, Felipe Poblete, Juan C Pozo
We consider the Kadomtsev–Petviashvili (KP) equations posed on R2 . For both models, we provide sequential in time asymptotic descriptions of solutions obtained from arbitrarily large initial data, inside regions of the plane not containing lumps or line solitons, and under minimal regularity assumptions. The proof involves the introduction of two new virial identities adapted to the KP dynamics. This
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Gevrey and Gelfand–Shilov smoothing effect for the spatially inhomogeneous Landau equation with hard potentials Nonlinearity (IF 1.7) Pub Date : 2024-04-02 Hao-Guang Li
In this work, we study the Cauchy problem of the spatially inhomogeneous Landau equation with hard potential in torus. It is showed that the smooth mild solution near Maxwellians to the Cauchy problem enjoys a Gelfand–Shilov regularizing effect in velocity variable and Gevrey smoothness property in space variable.
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Stability and bifurcation diagram for a shadow Gierer–Meinhardt system in one spatial dimension Nonlinearity (IF 1.7) Pub Date : 2024-04-02 Yuki Kaneko, Yasuhito Miyamoto, Tohru Wakasa
We are concerned with a Neumann problem of a shadow system of the Gierer–Meinhardt model in an interval I=(0,1) . A stationary problem is studied, and we consider the diffusion coefficient ɛ > 0 as a bifurcation parameter. Then a complete bifurcation diagram of the stationary solutions is obtained, and a stability of every stationary solution is determined. In particular, for each n⩾1 , two branches
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Shadowing for nonuniformly hyperbolic maps in Hilbert spaces Nonlinearity (IF 1.7) Pub Date : 2024-03-28 Xiankun Ren, Yunhua Zhou
We prove a shadowing lemma for nonuniformly hyperbolic maps in Hilbert spaces. As applications, we firstly prove that the positive Lyapunov exponents of a hyperbolic ergodic measure µ can be approximated by positive Lyapunov exponents of atomic measures on hyperbolic periodic orbits; secondly, give an upper estimation of metric entropy by using the exponential growth rate of the number of such periodic
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Microscopic derivation of Vlasov–Dirac–Benney equation with short-range pair potentials Nonlinearity (IF 1.7) Pub Date : 2024-03-28 Manuela Feistl, Peter Pickl
We present a probabilistic proof of the mean-field limit and propagation of chaos of a N-particle system in three dimensions with pair potentials of the form N3β−1ϕ(Nβx) for β∈[0,17] and ϕ∈ L∞(R3)∩L1(R3) . In particular, for typical initial data, we show convergence of the Newtonian trajectories to the characteristics of the Vlasov–Dirac–Benney system with delta-like interactions. The proof is based
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Singularity formation for the cylindrically symmetric rotating relativistic Euler equations of Chaplygin gases Nonlinearity (IF 1.7) Pub Date : 2024-03-28 Yanbo Hu, Houbin Guo
This paper studies the formation of singularities in smooth solutions of the relativistic Euler equations of Chaplygin gases with cylindrically symmetric rotating structures. This is a nonhomogeneous hyperbolic system with highly nonlinear structures and fully linearly degenerating characteristic fields. We introduce a pair of auxiliary functions and use the characteristic decomposition technique to
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Continua and persistence of periodic orbits in ensembles of oscillators Nonlinearity (IF 1.7) Pub Date : 2024-03-22 R Ronge, M A Zaks, T Pereira
Certain systems of coupled identical oscillators like the Kuramoto–Sakaguchi or the active rotator model possess the remarkable property of being Watanabe–Strogatz integrable. We prove that such systems, which couple via a global order parameter, feature a normally attracting invariant manifold that is foliated by periodic orbits. This allows us to study the asymptotic dynamics of general ensembles
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Travelling modulating pulse solutions with small tails for a nonlinear wave equation in periodic media Nonlinearity (IF 1.7) Pub Date : 2024-03-22 Tomáš Dohnal, Dmitry E Pelinovsky, Guido Schneider
Travelling modulating pulse solutions consist of a small amplitude pulse-like envelope moving with a constant speed and modulating a harmonic carrier wave. Such solutions can be approximated by solitons of an effective nonlinear Schrödinger equation arising as the envelope equation. We are interested in a rigorous existence proof of such solutions for a nonlinear wave equation with spatially periodic
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The plasma-charge model in a convex domain Nonlinearity (IF 1.7) Pub Date : 2024-03-21 Jingpeng Wu
The aim of this paper is to study the initial-boundary value problems of a Vlasov type system in a convex domain, so called the plasma-charge model, in which there are two kinds of singular sets, one caused by the boundary effect, the other by the heavy point charges. We prove the local existence of classical solutions for the case that the point charges are moving and global existence of classical
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Stability for a system of the 2D incompressible magneto-micropolar fluid equations with partial mixed dissipation Nonlinearity (IF 1.7) Pub Date : 2024-03-18 Hongxia Lin, Sen Liu, Heng Zhang, Qing Sun
This paper focuses on the 2D incompressible anisotropic magneto-micropolar fluid equations with vertical dissipation, horizontal magnetic diffusion, and horizontal vortex viscosity. The goal is to investigate the stability of perturbations near a background magnetic field in the 2D magneto-micropolar fluid equations. Two main results are obtained. The first result is based on the linear system. Global
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Numerical study on how advection delays and removes singularity formation in the Navier–Stokes equations Nonlinearity (IF 1.7) Pub Date : 2024-03-18 Koji Ohkitani
We numerically study a distorted version of the Euler and Navier–Stokes equations, which are obtained by depleting the advection term systematically. It is known that in the inviscid case some solutions blow up in finite time when advection is totally discarded, Constantin (1986 Commun. Math. Phys. 104 311–26). Taking a pair of orthogonally offset vortex tubes and the Taylor–Green vortex as initial
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Hard congestion limit of the dissipative Aw–Rascle system Nonlinearity (IF 1.7) Pub Date : 2024-03-14 N Chaudhuri, L Navoret, C Perrin, E Zatorska
In this study, we analyse the famous Aw–Rascle system in which the difference between the actual and the desired velocities (the offset function) is a gradient of a singular function of the density. This leads to a dissipation in the momentum equation which vanishes when the density is zero. The resulting system of PDEs can be used to model traffic or suspension flows in one dimension with the maximal
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Critical transitions for scalar nonautonomous systems with concave nonlinearities: some rigorous estimates Nonlinearity (IF 1.7) Pub Date : 2024-03-14 Iacopo P Longo, Carmen Núñez, Rafael Obaya
The global dynamics of a nonautonomous Carathéodory scalar ordinary differential equation x′=f(t,x) , given by a function f which is concave in x, is determined by the existence or absence of an attractor-repeller pair of hyperbolic solutions. This property, here extended to a very general setting, is the key point to classify the dynamics of an equation which is a transition between two nonautonomous
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Numerical study of the Serre–Green–Naghdi equations in 2D * Nonlinearity (IF 1.7) Pub Date : 2024-03-13 Sergey Gavrilyuk, Christian Klein
A detailed numerical study of solutions to the Serre–Green–Naghdi (SGN) equations in 2D with vanishing curl of the velocity field is presented. The transverse stability of line solitary waves, 1D solitary waves being exact solutions of the 2D equations independent of the second variable, is established numerically. The study of localized initial data as well as crossing 1D solitary waves does not give
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Stability theory for two-lobe states on the tadpole graph for the NLS equation Nonlinearity (IF 1.7) Pub Date : 2024-03-13 Jaime Angulo Pava
The aim of this work is to present new spectral tools for studying the orbital stability of standing waves solutions for the nonlinear Schrödinger equation (NLS) with power nonlinearity on a tadpole graph, namely, a graph consisting of a circle with a half-line attached at a single vertex. By considering δ-type boundary conditions at the junction and bound states with a positive two-lobe profile, the
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Thermocapillary thin films: periodic steady states and film rupture Nonlinearity (IF 1.7) Pub Date : 2024-03-13 Gabriele Bruell, Bastian Hilder, Jonas Jansen
We study stationary, periodic solutions to the thermocapillary thin-film model 0,\ x\in \mathbb{R},$?> ∂th+∂xh3∂x3h−g∂xh+Mh21+h2∂xh=0,t>0, x∈R, which can be derived from the Bénard–Marangoni problem via a lubrication approximation. When the Marangoni number M increases beyond a critical value M∗ , the constant solution becomes spectrally unstable via a (conserved) long-wave instability and periodic
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Monge–Ampère geometry and vortices Nonlinearity (IF 1.7) Pub Date : 2024-03-12 Lewis Napper, Ian Roulstone, Vladimir Rubtsov, Martin Wolf
We introduce a new approach to Monge–Ampère geometry based on techniques from higher symplectic geometry. Our work is motivated by the application of Monge–Ampère geometry to the Poisson equation for the pressure that arises for incompressible Navier–Stokes flows. Whilst this equation constitutes an elliptic problem for the pressure, it can also be viewed as a non-linear partial differential equation
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A nonlinear system to model communication between yeast cells during their mating process Nonlinearity (IF 1.7) Pub Date : 2024-03-12 Vincent Calvez, Thomas Lepoutre, Nicolas Meunier, Nicolas Muller
In this work, we develop a model to describe some aspects of communication between yeast cells. It consists in a coupled system of two one-dimensional non-linear advection-diffusion equations in which the advective field is given by the Hilbert transform. We give some sufficient condition for the blow-up in finite time of the coupled system (formation of a singularity). We provide a biological interpretation
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Phase transitions in the fractional three-dimensional Navier–Stokes equations Nonlinearity (IF 1.7) Pub Date : 2024-03-11 Daniel W Boutros, John D Gibbon
The fractional Navier–Stokes equations on a periodic domain [0,L]3 differ from their conventional counterpart by the replacement of the −νΔu Laplacian term by νsAsu , where A=−Δ is the Stokes operator and νs=νL2(s−1) is the viscosity parameter. Four critical values of the exponent s⩾0 have been identified where functional properties of solutions of the fractional Navier–Stokes equations change. These
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Formation of singularities in plasma ion dynamics Nonlinearity (IF 1.7) Pub Date : 2024-03-11 Junsik Bae, Junho Choi, Bongsuk Kwon
We study the formation of singularity for the Euler–Poisson system equipped with the Boltzmann relation, which describes the dynamics of ions in an electrostatic plasma. In general, it is known that smooth solutions to nonlinear hyperbolic equations fail to exist globally in time. We establish criteria for C 1 blow-up of the Euler–Poisson system, both for the isothermal and pressureless cases. In particular
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Regularity estimates for fully nonlinear integro-differential equations with nonhomogeneous degeneracy Nonlinearity (IF 1.7) Pub Date : 2024-03-05 Pêdra D S Andrade, Disson S dos Prazeres, Makson S Santos
We investigate the regularity of the solutions for a class of degenerate/singular fully nonlinear nonlocal equations. In the degenerate scenario, we establish that there exists at least one viscosity solution of class Cloc1,α , for some constant α∈(0,1) . In addition, under suitable conditions on degree of the operator σ, we prove regularity estimates in Hölder spaces for any viscosity solution. We
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A numerical study of rigidity of hyperbolic splittings in simple two-dimensional maps Nonlinearity (IF 1.7) Pub Date : 2024-03-04 Oscar F Bandtlow, Wolfram Just, Julia Slipantschuk
Chaotic hyperbolic dynamical systems enjoy a surprising degree of rigidity, a fact which is well known in the mathematics community but perhaps less so in theoretical physics circles. Low-dimensional hyperbolic systems are either conjugate to linear automorphisms, that is, dynamically equivalent to the Arnold cat map and its variants, or their hyperbolic structure is not smooth. We illustrate this
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The second iterate of the Muskat equation in supercritical spaces Nonlinearity (IF 1.7) Pub Date : 2024-03-04 Esteban Paduro
The ill-posedness of the Muskat problem in spaces that are supercritical with respect to scaling is studied. The paper’s main result establishes that for a sequence of approximations of the Muskat equation obtained via Taylor expansion, their corresponding second Picard’s iterate is discontinuous around the origin in a certain family of supercritical spaces approaching a critical space.
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Linear response for intermittent maps with critical point Nonlinearity (IF 1.7) Pub Date : 2024-03-04 Juho Leppänen
We consider a two-parameter family of maps Tα,β:[0,1]→[0,1] with a neutral fixed point and a non-flat critical point. Building on a cone technique due to Baladi and Todd, we show that for a class of Lq observables ϕ:[0,1]→R the bivariate map (α,β)↦∫01ϕdμα,β , where μα,β denotes the invariant SRB measure, is differentiable in a certain parameter region, and establish a formula for its directional derivative
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Gromov–Hausdorff variational principles and measure stability * * KL and CAM were partially supported by Basic Science Research Program through the NRF funded by the Ministry of Education of the Republic of Korea (Grant Number: 2022R1l1A3053628). Nonlinearity (IF 1.7) Pub Date : 2024-03-01 Keonhee Lee, C A Morales, Ngocthach Nguyen
Variational formulae for the Gromov–Hausdorff distances of compact metric spaces and their continuous maps are obtained. Also, a notion of µ-topological GH-stability on metric-measure spaces with probability µ is given. We prove that every expansive map with the weak µ-shadowing property (Lee and Rojas 2022 Russ. J. Nonlinear Dyn. 18 297–307) is µ-topologically GH-stable.
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Assouad type dimensions of infinitely generated self-conformal sets Nonlinearity (IF 1.7) Pub Date : 2024-02-29 Amlan Banaji, Jonathan M Fraser
We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of conformal contractions. Our focus is on the Assouad type dimensions, which give information about the local structure of sets. Under natural separation conditions, we prove a formula for the Assouad dimension and prove sharp bounds for the Assouad spectrum in terms of the Hausdorff
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Finite-time blow-up in hyperbolic Keller–Segel system of consumption type with logarithmic sensitivity Nonlinearity (IF 1.7) Pub Date : 2024-02-28 Jungkyoung Na
This paper deals with finite-time blow-up of a hyperbolic Keller–Segel system of consumption type with the logarithmic sensitivity 0\right)$?> ∂tρ=−χ∇⋅ρ∇logc,∂tc=−μcρχ,μ>0 in Rd(d⩾1) for nonvanishing initial data. This system is closely related to tumor angiogenesis, an important example of chemotaxis. Our singularity formation is not because c touches zero (which makes logc diverge) but due to the
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On uniqueness properties of solutions of the generalized fourth-order Schrödinger equations Nonlinearity (IF 1.7) Pub Date : 2024-02-27 Zachary Lee, Xueying Yu
In this paper, we study uniqueness properties of solutions to the generalized fourth-order Schrödinger equations in any dimension d of the following forms, i∂tu+∑j=1d∂xj4u=Vt,xu,andi∂tu+∑j=1d∂xj4u+Fu,u‾=0. We show that a linear solution u with fast enough decay in certain Sobolev spaces at two different times has to be trivial. Consequently, if the difference between two nonlinear solutions u 1 and
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Collapse dynamics for two-dimensional space-time nonlocal nonlinear Schrödinger equations Nonlinearity (IF 1.7) Pub Date : 2024-02-21 Justin T Cole, Abdullah M Aurko, Ziad H Musslimani
The question of collapse (blow-up) in finite time is investigated for the two-dimensional (non-integrable) space-time nonlocal nonlinear Schrödinger equations. Starting from the two-dimensional extension of the well known AKNS q,r system, three different cases are considered: (i) partial and full parity-time (PT) symmetric, (ii) reverse-time (RT) symmetric, and (iii) general q,r system. Through extensive
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Monotonic convergence of positive radial solutions for general quasilinear elliptic systems Nonlinearity (IF 1.7) Pub Date : 2024-02-20 Daniel Devine, Paschalis Karageorgis
We study the asymptotic behavior of positive radial solutions for quasilinear elliptic systems that have the form Δpu=c1|x|m1⋅g1v⋅|∇u|αin Rn,Δpv=c2|x|m2⋅g2v⋅g3|∇u|in Rn, where Δp denotes the p-Laplace operator, p > 1, n⩾2 , c1,c2>0 and m1,m2,α⩾0 . For a general class of functions gj which grow polynomially, we show that every non-constant positive radial solution (u, v) asymptotically approaches (u0
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A regularity result for the free boundary compressible Euler equations of a liquid Nonlinearity (IF 1.7) Pub Date : 2024-02-19 Linfeng Li
We derive a priori estimates for the compressible free boundary Euler equations in the case of a liquid without surface tension. We provide a new weighted functional framework which leads to the improved regularity of the flow map by using the Hardy inequality. One of main ideas is to decompose the initial density function. It is worth mentioning that in our analysis we do not need the higher order
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Exponential rate of decay of correlations of equilibrium states associated with non-uniformly expanding circle maps Nonlinearity (IF 1.7) Pub Date : 2024-02-19 Eduardo Garibaldi, Irene Inoquio-Renteria
In the context of expanding maps of the circle with an indifferent fixed point, understanding the joint behavior of dynamics and pairs of moduli of continuity (ω,Ω) may be a useful element for the development of equilibrium theory. Here we identify a particular feature of modulus Ω (precisely limx→0+supdΩ(dx)/Ω(d)=0 ) as a sufficient condition for the system to exhibit exponential decay of correlations
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Bounds on buoyancy driven flows with Navier-slip conditions on rough boundaries Nonlinearity (IF 1.7) Pub Date : 2024-02-15 Fabian Bleitner, Camilla Nobili
We consider two-dimensional Rayleigh–Bénard convection with Navier-slip and fixed temperature boundary conditions at the two horizontal rough walls described by the height function h. We prove rigorous upper bounds on the Nusselt number Nu which capture the dependence on the curvature of the boundary κ and the (non-constant) friction coefficient α explicitly. If h∈W2,∞ and κ satisfies a smallness condition
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Modeling the interplay of oscillatory synchronization and aggregation via cell–cell adhesion Nonlinearity (IF 1.7) Pub Date : 2024-02-13 Tilmann Glimm, Daniel Gruszka
We present a model of systems of cells with intracellular oscillators (‘clocks’). This is motivated by examples from developmental biology and from the behavior of organisms on the threshold to multicellularity. Cells undergo random motion and adhere to each other. The adhesion strength between neighbors depends on their clock phases in addition to a constant baseline strength. The oscillators are
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Revisiting the Kepler problem with linear drag using the blowup method and normal form theory Nonlinearity (IF 1.7) Pub Date : 2024-02-09 K Uldall Kristiansen
In this paper, we revisit the Kepler problem with linear drag. With dissipation, the energy and the angular momentum are both decreasing, but in Margheri et al (2017 Celest. Mech. Dyn. Astron. 127 35–48) it was shown that the eccentricity vector has a well-defined limit in the case of linear drag. This limiting eccentricity vector defines a conserved quantity, and in the present paper, we prove that
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Dihedral rings of patterns emerging from a Turing bifurcation Nonlinearity (IF 1.7) Pub Date : 2024-02-09 Dan J Hill, Jason J Bramburger, David J B Lloyd
Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when the patterns are strongly interacting. We prove that approximate strongly interacting patterns can emerge in various ring-like dihedral configurations, bifurcating
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Higgs fields, non-abelian Cauchy kernels and the Goldman symplectic structure Nonlinearity (IF 1.7) Pub Date : 2024-02-07 M Bertola, C Norton, G Ruzza
We consider the moduli space of vector bundles of rank n and degree ng over a fixed Riemann surface of genus g⩾2 with the explicit parametrization in terms of the Tyurin data. The ‘non-abelian’ theta divisor consists of bundles such that h1⩾1 . On the complement of this divisor we construct a non-abelian (i.e. matrix) Cauchy kernel explicitly in terms of the Tyurin data. With the additional datum of
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Strong convergence of the vorticity and conservation of the energy for the α-Euler equations Nonlinearity (IF 1.7) Pub Date : 2024-02-06 Stefano Abbate, Gianluca Crippa, Stefano Spirito
In this paper, we study the convergence of solutions of the α-Euler equations to solutions of the Euler equations on the two-dimensional torus. In particular, given an initial vorticity ω 0 in Lxp for p∈(1,∞) , we prove strong convergence in Lt∞Lxp of the vorticities q α , solutions of the α-Euler equations, towards a Lagrangian and energy-conserving solution of the Euler equations. Furthermore, if
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Bifurcation and regularity analysis of the Schrödinger-Poisson equation Nonlinearity (IF 1.7) Pub Date : 2024-02-05 Patrizia Pucci, Linlin Wang, Binlin Zhang
The aim of this paper is to present bifurcation results for (weak) solutions of the Schrödinger-Poisson system in R3 , involving subcritical and critical nonlinearities and using the global bifurcation theorem. Furthermore, we establish the existence of unbounded components of (weak) solutions, which bifurcate from trivial solutions and from infinity, respectively. The novelties of the paper lie in
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Quasi-periodic waves to the defocusing nonlinear Schrödinger equation Nonlinearity (IF 1.7) Pub Date : 2024-02-02 Ying-Nan Zhang, Xing-Biao Hu, Jian-Qing Sun
A direct approach for the quasi-periodic wave solutions to the defocusing nonlinear Schrödinger equation is proposed based on the theta functions and Hirota’s bilinear method. We transform the problem into a system of algebraic equations, which can be formulated into a least squares problem and then solved by using numerical iterative methods. A rigorous asymptotic analysis demonstrates that these
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Boundary asymptotics of non-intersecting Brownian motions: Pearcey, Airy and a transition Nonlinearity (IF 1.7) Pub Date : 2024-01-30 Thorsten Neuschel, Martin Venker
We study n non-intersecting Brownian motions, corresponding to the eigenvalues of an n × n Hermitian Brownian motion. At the boundary of their limit shape we find that only three universal processes can arise: the Pearcey process close to merging points, the Airy line ensemble at edges and a novel determinantal process describing the transition from the Pearcey process to the Airy line ensemble. The
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Backpropagation in hyperbolic chaos via adjoint shadowing Nonlinearity (IF 1.7) Pub Date : 2024-01-30 Angxiu Ni
To generalise the backpropagation method to both discrete-time and continuous-time hyperbolic chaos, we introduce the adjoint shadowing operator S acting on covector fields. We show that S can be equivalently defined as: S is the adjoint of the linear shadowing operator S; S is given by a ‘split then propagate’ expansion formula; S(ω) is the only bounded inhomogeneous adjoint solution of ω.By (a),
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New Liouville type theorems for the stationary Navier–Stokes, MHD, and Hall–MHD equations Nonlinearity (IF 1.7) Pub Date : 2024-01-30 Youseung Cho, Jiří Neustupa, Minsuk Yang
We establish new Liouville-type theorems for weak solutions of the stationary Navier–Stokes equations, stationary magnetohydrodynamics (MHD) equations and stationary Hall–MHD equations under some conditions on the growth of certain Lebesgue norms of the velocity and the magnetic field.