Dynamics of Partial Differential Equations

Volume 12 (2015)

Number 2

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

Pages: 97 – 113

DOI: http://dx.doi.org/10.4310/DPDE.2015.v12.n2.a1

Author

H. Inci (School of Engineering, Zurich University of Applied Sciences (ZHAW), Winterthur, Switzerland)

Abstract

In this paper we consider the incompressible Euler equation on the Sobolev space $H^s (\mathbb{R}^n), s \gt n/2 + 1$, and show that for any $T \gt 0$ 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.

Keywords

Euler equations, regularity of the solution map, nowhere differentiable

2010 Mathematics Subject Classification

35-xx, 76-xx

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Published 9 June 2015