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

Hasan Inci

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

Analysis of PDEs 2013-02-04 v1

Authors: Hasan Inci

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.

Keywords

incompressible Euler equation solution map regularity Sobolev space nowhere locally uniformly continuous nowhere differentiable

Cite

@article{arxiv.1302.0209,
  title  = {On the regularity of the solution map of the incompressible Euler equation},
  author = {Hasan Inci},
  journal= {arXiv preprint arXiv:1302.0209},
  year   = {2013}
}

Comments

arXiv admin note: text overlap with arXiv:1301.5994

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