English

Ill-posedness of the incompressible Euler equations in the $C^1$ space

Analysis of PDEs 2014-05-09 v1

Abstract

We prove that the 2D Euler equations are not locally well-posed in C1C^1. Our approach relies on the technique of Lagrangian deformations and norm inflation of Bourgain and Li. We show that the assumption that the data-to-solution map is continuous in C1C^1 leads to a contradiction with a well-posedness result in W1,pW^{1,p} of Kato and Ponce.

Keywords

Cite

@article{arxiv.1405.1943,
  title  = {Ill-posedness of the incompressible Euler equations in the $C^1$ space},
  author = {Gerard Misiołek and Tsuyoshi Yoneda},
  journal= {arXiv preprint arXiv:1405.1943},
  year   = {2014}
}