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

Abstract

In this paper we consider the incompressible Euler equation on the Sobolev space $H^s({\mathbb{R}}^n)$, $s>n/2+1$, 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.

arXiv admin note: text overlap with arXiv:1301.5994