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arXiv · 2507.02247

Ill-posedness and inviscid limit of basic equations of fluid dynamics in Besov spaces

Jinlu Li·Xing Wu·Yanghai Yu
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Abstract

In this paper, we consider the Cauchy problem to the basic equations of fluid dynamics on the torus. Firstly, we construct a new initial data and provide a simple proof on the ill-posedness of $B^s_{p,\infty}$ solution of the Euler equations and the surface quasi-geostrophic equation, which covers the results obtained by Cheskidov-Shvydkoy \cite{CS} and Misio{\l}ek-Yoneda \cite{MY}. Secondly, we prove the failure of the $B^s_{p,\infty}$-convergence in the inviscid limit for both the Navier-Stokes equations and the surface quasi-geostrophic equation.

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Jinlu Li, Xing Wu, Yanghai Yu. 2025-07-03. Ill-posedness and inviscid limit of basic equations of fluid dynamics in Besov spaces. https://arxiv.org/abs/2507.02247

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