Non-convergence of the Navier–Stokes Equations Toward the Euler Equations in the Endpoint Besov Spaces

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发表日期：

2025年9月4日

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Yanghai Yu,
Jinlu Li

摘要

In this paper, we consider the inviscid limit problem to the higher dimensional incompressible Navier–Stokes equations in the whole space. It was proved in [Guo et al. J. Funct. Anal. 276:2821–2830, 2019] that given initial data \(u_0\in B^{s}_{p,r}\) with \(1\le r<\infty\) , the solution of the Navier–Stokes equations converges strongly in \(B^{s}_{p,r}\) to the solution of the Euler equations as the viscosity parameter tends to zero. In the case when \(r=\infty\) , we prove the failure of the \(B^{s}_{p,\infty }\) -convergence of the Navier-Stokes equations toward the Euler equations in the inviscid limit.