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 . 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 leads to a contradiction with a well-posedness result in 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}
}