- Turkish Journal of Mathematics
- Vol: 43 Issue: 6
- On the regularity of the solution map of the Euler-Poisson system
On the regularity of the solution map of the Euler-Poisson system
Authors : Hasan Inci
Pages : 2767-2781
View : 8 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :In this paper we consider the Euler--Poisson system (describing a plasma consisting of positive ions with a negligible temperature and massless electrons in thermodynamical equilibrium) on the Sobolev spaces $H^s(\mathbb{R}^3)$, $s > 5/2$. 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 $\mathbb{R}^3$.Keywords : Euler-Poisson system, solution map