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

In-Jee Jeong; Junha Kim

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

Analysis of PDEs 2022-07-19 v2

Authors: In-Jee Jeong , Junha Kim

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.

Keywords

incompressible euler equations ill-posedness critical sobolev spaces cauchy problem lorentz spaces

Cite

@article{arxiv.2111.14078,
  title  = {A simple proof of ill-posedness for incompressible Euler equations in critical Sobolev spaces},
  author = {In-Jee Jeong and Junha Kim},
  journal= {arXiv preprint arXiv:2111.14078},
  year   = {2022}
}

Comments

To appear in J. Funct. Anal

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