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Inviscid limit for stochastic second-grade fluid equations

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Abstract

We consider in a smooth bounded and simply connected two dimensional domain the convergence in the \(L^2\) norm, uniformly in time, of the solution of the stochastic second-grade fluid equations with transport noise and no-slip boundary conditions to the solution of the corresponding Euler equations. We prove, that assuming proper regularity of the initial conditions of the Euler equations and a proper behavior of the parameters \(\nu \) and \(\alpha \), then the inviscid limit holds without requiring a particular dissipation of the energy of the solutions of the second-grade fluid equations in the boundary layer.

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Acknowledgements

I want to thank Professor Franco Flandoli and Professor Edriss Titi for useful discussions and valuable insights into the subject. I also would like to express my sincere gratitude to the referees and the editor for their careful reading and helpful suggestions which improved drastically the presentation of the paper from its initial version.

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  1. Scuola Normale Superiore, Piazza dei Cavalieri, 7, 56126, Pisa, Italy

    Eliseo Luongo

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Luongo, E. Inviscid limit for stochastic second-grade fluid equations. Stoch PDE: Anal Comp 12, 1046–1099 (2024). https://doi.org/10.1007/s40072-023-00303-y

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