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arXiv · 1405.1943

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

Gerard Misiołek·Tsuyoshi Yoneda
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Abstract

We prove that the 2D Euler equations are not locally well-posed in $C^1$. 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 $C^1$ leads to a contradiction with a well-posedness result in $W^{1,p}$ of Kato and Ponce.

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Gerard Misiołek, Tsuyoshi Yoneda. 2014-05-08. Ill-posedness of the incompressible Euler equations in the $C^1$ space. https://arxiv.org/abs/1405.1943

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