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Stability for the Magnetic Bénard System with Partial Dissipation J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-04-17 Yuzhu Wang, Yuhang Zhang, Xiaoping Zhai
In this paper, we prove the global existence and stability of the magnetic Bénard system with partial dissipation on perturbations near a background magnetic field in \({\mathbb {T}}^d (d=2,3)\). If there is no velocity dissipation, the stability result provides a significant example for the stabilizing effects of the magnetic field on electrically conducting fluids. In addition, we obtain an explicit
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On the Steadiness of Symmetric Solutions to Two Dimensional Dispersive Models J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-04-15 Long Pei, Fengyang Xiao, Pan Zhang
In this paper, we consider the steadiness of symmetric solutions to two dispersive models in shallow water and hyperelastic mechanics, respectively. These models are derived previously in the two-dimensional setting and can be viewed as the generalization of the Camassa–Holm and Kadomtsev–Petviashvili equations. For these two models, we prove that the symmetry of classical solutions implies steadiness
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Approximation of a Solution to the Stationary Navier–Stokes Equations in a Curved Thin Domain by a Solution to Thin-Film Limit Equations J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-04-15 Tatsu-Hiko Miura
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Navier–Stokes Equations in the Half Space with Non Compatible Data J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-04-06 Andrea Argenziano, Marco Cannone, Marco Sammartino
This paper considers the Navier–Stokes equations in the half plane with Euler-type initial conditions, i.e., initial conditions with a non-zero tangential component at the boundary. Under analyticity assumptions for the data, we prove that the solution exists for a short time independent of the viscosity. We construct the Navier–Stokes solution through a composite asymptotic expansion involving solutions
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A Sharp Version of the Benjamin and Lighthill Conjecture for Steady Waves with Vorticity J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-04-06 Evgeniy Lokharu
We give a complete proof of the classical Benjamin and Lighthill conjecture for arbitrary two-dimensional steady water waves with vorticity. We show that the flow force constant of an arbitrary smooth solution is bounded by the flow force constants for the corresponding conjugate laminar flows. We prove these inequalities without any assumptions on the geometry of the surface profile and put no restrictions
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A Nonlinear Elliptic PDE from Atmospheric Science: Well-Posedness and Regularity at Cloud Edge J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-03-29 Antoine Remond-Tiedrez, Leslie M. Smith, Samuel N. Stechmann
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Mathematical Analysis of a Diffuse Interface Model for Multi-phase Flows of Incompressible Viscous Fluids with Different Densities J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-03-29 Helmut Abels, Harald Garcke, Andrea Poiatti
We analyze a diffuse interface model for multi-phase flows of N incompressible, viscous Newtonian fluids with different densities. In the case of a bounded and sufficiently smooth domain existence of weak solutions in two and three space dimensions and a singular free energy density is shown. Moreover, in two space dimensions global existence for sufficiently regular initial data is proven. In three
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Non-Uniqueness and Energy Dissipation for 2D Euler Equations with Vorticity in Hardy Spaces J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-03-28 Miriam Buck, Stefano Modena
We construct by convex integration examples of energy dissipating solutions to the 2D Euler equations on \({\mathbb {R}}^2\) with vorticity in the Hardy space \(H^p({\mathbb {R}}^2)\), for any \(2/3
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An Efficient Second-Order Algorithm Upon MAC Scheme for Nonlinear Incompressible Darcy–Brinkman–Forchheimer Model J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-03-28 Pengshan Wang, Wei Liu, Gexian Fan, Yingxue Song
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Augmented Lagrangian Acceleration of Global-in-Time Pressure Schur Complement Solvers for Incompressible Oseen Equations J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-03-28 Christoph Lohmann, Stefan Turek
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On the Local Existence of Solutions to the compressible Navier–Stokes-Wave System with a Free Interface J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-03-15 Igor Kukavica, Linfeng Li, Amjad Tuffaha
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Conjugate Points Along Kolmogorov Flows on the Torus J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-03-07
Abstract The geodesics in the group of volume-preserving diffeomorphisms (volumorphisms) of a manifold M, for a Riemannian metric defined by the kinetic energy, can be used to model the movement of ideal fluids in that manifold. The existence of conjugate points along such geodesics reveal that these cease to be infinitesimally length-minimizing between their endpoints. In this work, we focus on the
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Periodic Capillary-Gravity Water Waves of Small Amplitude J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-02-28 Qixiang Li, JinRong Wang
In this paper, we investigate two-dimensional capillary-gravity water waves of small amplitude, which propagate over a flat bed. We prove the existence of a local curve of solutions by using the Crandall–Rabinowitz local bifurcation theory, and show the uniqueness for the capillary-gravity water waves. Furthermore, we recover the dispersion relation for the constant vorticity setting. Moreover, we
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Blow-up Analysis for the $${\varvec{ab}}$$ -Family of Equations J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-02-24 Wenguang Cheng, Ji Lin
This paper investigates the Cauchy problem for the ab-family of equations with cubic nonlinearities, which contains the integrable modified Camassa–Holm equation (\(a = \frac{1}{3}\), \(b = 2\)) and the Novikov equation (\(a = 0\), \(b = 3\)) as two special cases. When \(3a + b \ne 3\), the ab-family of equations does not possess the \(H^1\)-norm conservation law. We give the local well-posedness results
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Linear Instability of Symmetric Logarithmic Spiral Vortex Sheets J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-02-23
Abstract We consider Alexander spirals with \(M\ge 3\) branches, that is symmetric logarithmic spiral vortex sheets. We show that such vortex sheets are linearly unstable in the \(L^\infty \) (Kelvin–Helmholtz) sense, as solutions to the Birkhoff–Rott equation. To this end we consider Fourier modes in a logarithmic variable to identify unstable solutions with polynomial growth in time.
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Temporal Regularity of Symmetric Stochastic p-Stokes Systems J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-02-21 Jörn Wichmann
We study the symmetric stochastic p-Stokes system, \(p \in (1,\infty )\), in a bounded domain. The results are two-fold: First, we show that in the context of analytically weak solutions, the stochastic pressure—related to non-divergence free stochastic forces—enjoys almost \(-1/2\) temporal derivatives on a Besov scale. Second, we verify that the velocity u of strong solutions obeys 1/2 temporal derivatives
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On the Weak Solutions to the Multicomponent Reactive Flows Driven by Non-conservative Boundary Conditions J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-02-20
Abstract We propose a new concept of weak solutions to the multicomponent reactive flows driven by large boundary data. When the Gibbs’ equation incorporates the species mass fractions, we establish the global-in-time existence of weak solutions for any finite energy initial data. Moreover, if the classical solutions exist, the weak solutions coincide with them in the same time interval.
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Global Solutions of 3D Isentropic Compressible Navier–Stokes Equations with Two Slow Variables J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-02-19 NanNan Yang
Motivated by Lu and Zhang (J Differ Equ 376:406–468, 2023), we prove the global existence of solutions to the three-dimensional isentropic compressible Navier–Stokes equations with smooth initial data slowly varying in two directions. In such a setting, the \(L^2\)-norms of the initial data are of order \(O(\varepsilon ^{-1})\), which are large.
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Stability of Time-Dependent Motions for Fluid–Rigid Ball Interaction J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-02-19 Toshiaki Hishida
We aim at the stability of time-dependent motions, such as time-periodic ones, of a rigid body in a viscous fluid filling the exterior to it in 3D. The fluid motion obeys the incompressible Navier–Stokes system, whereas the motion of the body is governed by the balance for linear and angular momentum. Both motions are affected by each other at the boundary. Assuming that the rigid body is a ball, we
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On a Stokes System Arising in a Free Surface Viscous Flow of a Horizontally Periodic Fluid with Fractional Boundary Operators J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-02-12
Abstract In this note we investigate the initial-boundary value problem for a Stokes system arising in a free surface viscous flow of a horizontally periodic fluid with fractional boundary operators. We derive an integral representation of solutions by making use of the multiple Fourier series. Moreover, we demonstrate a unique solvability in the framework of the Sobolev space of \(L^2\) -type.
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2D Voigt Boussinesq Equations J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-02-02 Mihaela Ignatova
We consider a critical conservative Voigt regularization of the 2D incompressible Boussinesq system on the torus. We prove the existence and uniqueness of global smooth solutions and their convergence in the smooth regime to the Boussinesq solution when the regularizations are removed. We also consider a range of mixed (subcritical–supercritical) Voigt regularizations for which we prove the existence
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Almost Sure Well-Posedness for Hall MHD J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-01-29
Abstract We consider the magnetohydrodynamics system with Hall effect accompanied with initial data in supercritical Sobolev space. Via an appropriate randomization of the supercritical initial data, both local and small data global well-posedness for the system are obtained almost surely in critical Sobolev space.
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Initial-Boundary Value Problems for One-Dimensional pth Power Viscous Reactive Gas with Density-Dependent Viscosity J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-01-29 Yongkai Liao
Although there are many results on the global solvability and the precise description of the large time behaviors of solutions to the initial-boundary value/Cauchy problem of the one-dimensional pth power viscous reactive gas with positive constant viscosity, no result is available up to now for the corresponding problems with density-dependent viscosity. The main purpose of this paper is to study
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Diffusion Enhancement and Taylor Dispersion for Rotationally Symmetric Flows in Discs and Pipes J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-01-27 Michele Coti Zelati, Michele Dolce, Chia-Chun Lo
In this note, we study the long-time dynamics of passive scalars driven by rotationally symmetric flows. We focus on identifying precise conditions on the velocity field in order to prove enhanced dissipation and Taylor dispersion in three-dimensional infinite pipes. As a byproduct of our analysis, we obtain an enhanced decay for circular flows on a disc of arbitrary radius.
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Global Existence and Weak-Strong Uniqueness for Chemotaxis Compressible Navier–Stokes Equations Modeling Vascular Network Formation J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-01-18 Xiaokai Huo, Ansgar Jüngel
A model of vascular network formation is analyzed in a bounded domain, consisting of the compressible Navier–Stokes equations for the density of the endothelial cells and their velocity, coupled to a reaction-diffusion equation for the concentration of the chemoattractant, which triggers the migration of the endothelial cells and the blood vessel formation. The coupling of the equations is realized
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From Bipolar Euler-Poisson System to Unipolar Euler-Poisson One in the Perspective of Mass J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-01-16 Shuai Xi, Liang Zhao
The main purpose of this paper is to provide an effective procedure to study rigorously the relationship between unipolar and bipolar Euler-Poisson systems in the perspective of mass. Based on the fact that the mass of an electron is far less than that of an ion, we amplify this property by letting \(m_e/m_i\rightarrow 0\) and using two different singular limits to illustrate it, which are the zero-electron
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The Cauchy Problem for a Non-conservative Compressible Two-Fluid Model with Far Field Vacuum in Three Dimensions J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-01-03 Huanyao Wen, Xingyang Zhang
In this paper, we study the wellposedness of the Cauchy problem for a non-conservative compressible two-fluid model with density-dependent viscosity coefficients vanishing at far field in three dimensions. The non-conservative pressure term (an implicit function) and the degenerate viscosity coefficients due to the vanishing of the volume fractions and the densities are the main issues. To overcome
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Data Assimilation to the Primitive Equations with $$L^p$$ - $$L^q$$ -based Maximal Regularity Approach J. Math. Fluid Mech. (IF 1.3) Pub Date : 2024-01-04 Ken Furukawa
In this paper, we show a mathematical justification of the data assimilation of nudging type in \(L^p\)-\(L^q\) maximal regularity settings. We prove that the approximate solution of the primitive equations constructed by the data assimilation converges to the true solution with exponential order in the Besov space \(B^{2/q}_{q,p}(\Omega )\) for \(1/p + 1/q \le 1\) on the periodic layer domain \(\Omega
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Feedback Stabilization of a Two-Fluid Surface Tension System Modeling the Motion of a Soap Bubble at Low Reynolds Number: The Two-Dimensional Case J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-12-31 Sébastien Court
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Exact Solutions Modelling Nonlinear Atmospheric Gravity Waves J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-12-20 David Henry
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Microscopic Expression of Anomalous Dissipation in Passive Scalar Transport J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-12-11 Tomonori Tsuruhashi, Tsuyoshi Yoneda
We study anomalous dissipation from a microscopic viewpoint. In the work by Drivas et al. (Arch Ration Mech Anal 243(3):1151–1180, 2022), the property of anomalous dissipation provides the existence of non-unique weak solutions for a transport equation with a singular velocity field. In this paper, we reconsider this solution in terms of kinetic theory and clarify its microscopic property. Consequently
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Optimality of the Decay Estimate of Solutions to the Linearised Curl-Free Compressible Navier–Stokes Equations J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-11-14 Tsukasa Iwabuchi, Dáithí Ó hAodha
We discuss optimal estimates of solutions to the compressible Navier–Stokes equations in Besov norms. In particular, we consider the estimate of the curl-free part of the solution to the linearised equations, in the homogeneous case. We prove that our estimate is optimal in the \(L^\infty \)-norm by showing that the norm is bounded from below by the same decay rate.
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Well-Posedness of Solutions to Stochastic Fluid–Structure Interaction J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-11-16 Jeffrey Kuan, Sunčica Čanić
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A Method for Finding Exact Solutions to the 2D and 3D Euler–Boussinesq Equations in Lagrangian Coordinates J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-11-14 Tomi Saleva, Jukka Tuomela
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Nearly Toroidal, Periodic and Quasi-periodic Motions of Fluid Particles Driven by the Gavrilov Solutions of the Euler Equations J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-11-07 Pietro Baldi
We consider the smooth, compactly supported solutions of the steady 3D Euler equations of incompressible fluids constructed by Gavrilov (Geom Funct Anal (GAFA) 29(1):190–197, 2019), and we study the corresponding fluid particle dynamics. This is an ode analysis, which contributes to the description of Gavrilov’s vector field.
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Allen–Cahn–Navier–Stokes–Voigt Systems with Moving Contact Lines J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-10-31 Ciprian G. Gal, Maurizio Grasselli, Andrea Poiatti
We consider a diffuse interface model for an incompressible binary fluid flow. The model consists of the Navier–Stokes–Voigt equations coupled with the mass-conserving Allen–Cahn equation with Flory–Huggins potential. The resulting system is subject to generalized Navier boundary conditions for the (volume averaged) fluid velocity \({{\textbf {u}}}\) and to a dynamic contact line boundary condition
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Asymptotic Stability of Rarefaction Waves for Hyperbolized Compressible Navier–Stokes Equations J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-11-01 Yuxi Hu, Xuefang Wang
We consider a model of one dimensional isentropic compressible Navier–Stokes equations for which the classical Newtonian flow is replaced by a Maxwell flow. We establish the asymptotic stability of rarefaction waves for this model under some small conditions on initial perturbations and amplitude of the waves. The proof is based on \(L^2\) energy methods.
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Regularity Criterion for the 2D Inviscid Boussinesq Equations J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-10-17 Menghan Gong, Zhuan Ye
The question of whether the two-dimensional inviscid Boussinesq equations can develop a finite-time singularity from general initial data is a challenging open problem. In this paper, we obtain two new regularity criteria for the local-in-time smooth solution to the two-dimensional inviscid Boussinesq equations. Similar result is also valid for the nonlocal perturbation of the two-dimensional incompressible
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The Lagrangian Formulation for Wave Motion with a Shear Current and Surface Tension J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-10-17 Conor Curtin, Rossen Ivanov
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Global Existence of Strong Solutions and Serrin-Type Blowup Criterion for 3D Combustion Model in Bounded Domains J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-10-14 Jiawen Zhang
The combustion model is studied in three-dimensional (3D) smooth bounded domains with various types of boundary conditions. The global existence and uniqueness of strong solutions are obtained under the smallness of the gradient of initial velocity in some precise sense. Using the energy method with the estimates of boundary integrals, we obtain the a priori bounds of the density and velocity field
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The Stability and Decay for the 2D Incompressible Euler-Like Equations J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-10-11 Hongxia Lin, Qing Sun, Sen Liu, Heng Zhang
This paper is concerned with the two-dimensional incompressible Euler-like equations. More precisely, we consider the system with only damping in the vertical component equation. When the domain is the whole space \(\mathbb {R}^2\), it is well known that solutions of the incompressible Euler equations can grow rapidly in time while solutions of the Euler equations with full damping are stable. As the
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Mathematical Theory of Compressible Magnetohydrodynamics Driven by Non-conservative Boundary Conditions J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-10-07 Eduard Feireisl, Piotr Gwiazda, Young-Sam Kwon, Agnieszka Świerczewska-Gwiazda
We propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by ihomogeneous boundary data. The system of the underlying field equations is solvable globally in time in the out of equilibrium regime characteristic for turbulence. The weak solutions comply with the weak–strong uniqueness principle; they coincide with the classical solution of the problem as
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Fast Rotating Non-homogeneous Fluids in Thin Domains and the Ekman Pumping Effect J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-10-03 Marco Bravin, Francesco Fanelli
In this paper, we perform the fast rotation limit \(\varepsilon \rightarrow 0^+\) of the density-dependent incompressible Navier–Stokes–Coriolis system in a thin strip \(\Omega _\varepsilon :=\,{\mathbb {R}}^2\times \, \left. \right] -\ell _\varepsilon ,\ell _\varepsilon \left[ \right. \,\), where \(\varepsilon \in \,\left. \right] 0,1\left. \right] \) is the size of the Rossby number and \(\ell _\varepsilon
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Symmetrization and Local Existence of Strong Solutions for Diffuse Interface Fluid Models J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-09-28 Vincent Giovangigli, Yoann Le Calvez, Flore Nabet
We investigate compressible nonisothermal diffuse interface fluid models also termed capillary fluids. Such fluid models involve van der Waals’ gradient energy, Korteweg’s tensor, Dunn and Serrin’s heat flux as well as diffusive fluxes. The density gradient is added as an extra variable and the convective and capillary fluxes of the augmented system are identified by using the Legendre transform of
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Interaction of Finitely-Strained Viscoelastic Multipolar Solids and Fluids by an Eulerian Approach J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-09-23 Tomáš Roubíček
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Gevrey-Class-3 Regularity of the Linearised Hyperbolic Prandtl System on a Strip J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-09-01 Francesco De Anna, Joshua Kortum, Stefano Scrobogna
In the present paper, we address a physically-meaningful extension of the linearised Prandtl equations around a shear flow. Without any structural assumption, it is well-known that the optimal regularity of Prandtl is given by the class Gevrey 2 along the horizontal direction. The goal of this paper is to overcome this barrier, by dealing with the linearisation of the so-called hyperbolic Prandtl equations
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2D/3D Fully Decoupled, Unconditionally Energy Stable Rotational Velocity Projection Method for Incompressible MHD System J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-08-29 Ke Zhang, Haiyan Su, Demin Liu
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The Optimal Temporal Decay Rates for Compressible Hall-magnetohydrodynamics System J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-08-26 Shengbin Fu, Weiwei Wang
In this paper, we are interested in the global well-posedness of the strong solutions to the Cauchy problem on the compressible magnetohydrodynamics system with Hall effect. Moreover, we establish the convergence rates of the above solutions trending towards the constant equilibrium \(({\bar{\rho }},0,\bar{\textbf{B}})\), provided that the initial perturbation belonging to \(H^3({\mathbb {R}}^3) \cap
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Global existence and optimal decay rates for a generic non--conservative compressible two--fluid model J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-08-25 Yin Li, Huaqiao Wang, Guochun Wu, Yinghui Zhang
We investigate global existence and optimal decay rates of a generic non-conservative compressible two–fluid model with general constant viscosities and capillary coefficients, and our main purpose is three–fold: First, for any integer \(\ell \ge 3\), we show that the densities and velocities converge to their corresponding equilibrium states at the \(L^2\) rate \((1+t)^{-\frac{3}{4}}\), and the k(\(\in
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Correction to: On the Design of Global-in-Time Newton-Multigrid-Pressure Schur Complement Solvers for Incompressible Flow Problems J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-08-17 Christoph Lohmann, Stefan Turek
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Asymptotic Properties of Steady Plane Solutions of the Navier–Stokes Equations in a Cone-Like Domain J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-08-11 Lili Wang, Wendong Wang
Motivated by Gilbarg–Weinberger’s early work on asymptotic properties of steady plane solutions of the Navier–Stokes equations on a neighborhood of infinity (Gilbarg andWeinberger in Ann Scuola Norm Super Pisa Cl Sci 5(2):381–404, 1978), we investigate asymptotic properties of steady plane solutions of this system on any cone-like domain of \(\Omega _0=\{(r,\theta ); r>r_0, \theta \in (0,\theta _0)\}
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Motion of Rigid Bodies of Arbitrary Shape in a Viscous Incompressible Fluid: Wellposedness and Large Time Behaviour J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-08-07 Debayan Maity, Marius Tucsnak
We investigate the long-time behaviour of a coupled PDE–ODE system that describes the motion of a rigid body of arbitrary shape moving in a viscous incompressible fluid. We assume that the system formed by the rigid body and the fluid fills the entire space \(\mathbb {R}^{3}.\) We extend in this way our previous results which were limited to the case when the rigid body was a ball. More precisely,
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Global Regular Axially-Symmetric Solutions to the Navier–Stokes Equations with Small Swirl J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-08-04 Bernard Nowakowski, Wojciech M. Zajaczkowski
Axially symmetric solutions to the Navier–Stokes equations in a bounded cylinder are considered. On the boundary the normal component of the velocity and the angular components of the velocity and vorticity are assumed to vanish. If the norm of the initial swirl is sufficiently small, then the regularity of axially symmetric, weak solutions is shown. The key tool is a new estimate for the stream function
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On Unsteady Internal Flows of Incompressible Fluids Characterized by Implicit Constitutive Equations in the Bulk and on the Boundary J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-07-31 Miroslav Bulíček, Josef Málek, Erika Maringová
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Rigidity of Three-Dimensional Internal Waves with Constant Vorticity J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-07-25 Robin Ming Chen, Lili Fan, Samuel Walsh, Miles H. Wheeler
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Energy Conservation for the Generalized Surface Quasi-geostrophic Equation J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-07-24 Yanqing Wang, Yulin Ye, Huan Yu
In this paper, we consider the generalized surface quasi-geostrophic equation with the velocity v determined by \(v=\mathcal {R}^{\perp }\Lambda ^{\gamma -1}\theta ,\) \(0<\gamma < 2\). It is shown that the \(L^p\)-norm of weak solutions is conserved provided \(\theta \in L^{p+1}\left( 0,T; {B}^{\frac{\gamma }{3}}_{p+1, c(\mathbb {N})}\right) \) for \(0<\gamma <\frac{3}{2}\) or \(\theta \in L^{p+1}\left(
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Improved Well-Posedness for the Triple-Deck and Related Models via Concavity J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-07-21 David Gerard-Varet, Sameer Iyer, Yasunori Maekawa
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Localized Blow-Up Criterion for $$ C^{ 1, \alpha } $$ Solutions to the 3D Incompressible Euler Equations J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-07-19 Dongho Chae, Jörg Wolf
We prove a localized Beale–Kato–Majda type blow-up criterion for the 3D incompressible Euler equations in the Hölder space setting. More specifically, let \(v\in C([0, T); C^{ 1, \alpha } (\Omega ))\cap L^\infty (0, T; L^2(\Omega ))\) be a solution to the Euler equations in a domain \(\Omega \subset {\mathbb {R}}^3\). If there exists a ball \(B\subset \Omega \) such that \( \int \limits \nolimits _{0}^T
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Spatially Quasi-Periodic Solutions of the Euler Equation J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-06-30 Xu Sun, Peter Topalov
We develop a framework for studying quasi-periodic maps and diffeomorphisms on \({\mathbb {R}}^n\). As an application, we prove that the Euler equation is locally well posed in a space of quasi-periodic vector fields on \({\mathbb {R}}^n\). In particular, the equation preserves the spatial quasi-periodicity of the initial data. Several results on the analytic dependence of solutions on the time and
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Global Boundedness to a 3D Chemotaxis–Stokes System with Porous Medium Cell Diffusion and General Sensitivity Under Dirichlet Signal Boundary Condition J. Math. Fluid Mech. (IF 1.3) Pub Date : 2023-07-01 Yu Tian, Zhaoyin Xiang
In this paper, we construct a globally bounded weak solution for the initial-boundary value problem of a three-dimensional chemotaxis–Stokes system with porous medium cell diffusion \(\Delta n^m\) and inhomogeneous Dirichlet signal boundary for each \(m>\frac{13}{12}\). Compared with the quite well-developed solvability for the no-flux signal boundary value with \(m>\frac{7}{6}\) (Winkler in Calc Var