On the regularity of the solution map of the Euler-Poisson system

Hasan Inci

On the regularity of the solution map of the Euler-Poisson system

Analysis of PDEs 2018-06-14 v2

Authors: Hasan Inci

Abstract

In this paper we consider the Euler-Poisson system (describing a plasma made of ions with a negligible ion temperature) on the Sobolev spaces $H^s(\R^3)$ , $s > 5/2$ . Using a geometric approach we show that for any time $T > 0$ the corresponding solution map, $(\rho_0,u_0) \mapsto (\rho(T),u(T))$ , is nowhere locally uniformly continuous. On the other hand it turns out that the trajectories of the ions are analytic curves in $\R^3$ .

Keywords

euler-poisson system sobolev spaces solution map uniform continuity analytic trajectories

Cite

@article{arxiv.1806.04439,
  title  = {On the regularity of the solution map of the Euler-Poisson system},
  author = {Hasan Inci},
  journal= {arXiv preprint arXiv:1806.04439},
  year   = {2018}
}

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