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arXiv · 2111.14078

A simple proof of ill-posedness for incompressible Euler equations in critical Sobolev spaces

In-Jee Jeong·Junha Kim
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Abstract

We provide a simple proof that the Cauchy problem for the incompressible Euler equations in $\mathbb{R}^{d}$ with any $d\ge3$ is ill-posed in critical Sobolev spaces, extending an earlier work of Bourgain and Li in the case $d = 3$. The ill-posedness is shown for certain critical Lorentz spaces as well.

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In-Jee Jeong, Junha Kim. 2021-11-28. A simple proof of ill-posedness for incompressible Euler equations in critical Sobolev spaces. https://arxiv.org/abs/2111.14078

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