On the regularity of the solution map of the incompressible Euler equation

Hasan Inci

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arXiv · 1302.0209

On the regularity of the solution map of the incompressible Euler equation

Hasan Inci

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Abstract

In this paper we consider the incompressible Euler equation on the Sobolev space $H^s(\R^n)$, $s > n/2+1$, and show that for any $T > 0$ its solution map $u_0 \mapsto u(T)$, mapping the initial value to the value at time $T$, is nowhere locally uniformly continuous and nowhere differentiable.

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Hasan Inci. 2013-02-01. On the regularity of the solution map of the incompressible Euler equation. https://arxiv.org/abs/1302.0209

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