Existence and uniqueness of two dimensional Euler-Poisson system and WKB approximation to the nonlinear Schrödinger-Poisson system

Satoshi Masaki, Takayoshi Ogawa

Research output: Contribution to journalArticle

Abstract

In this paper, we study a dispersive Euler-Poisson system in two dimensional Euclidean space. Our aim is to show unique existence and the zero-dispersion limit of the time-local weak solution. Since one may not use dispersive structure in the zero-dispersion limit, when reducing the regularity, lack of critical embedding H1 ⊆ L becomes a bottleneck. We hence employ an estimate on the best constant of the Gagliardo-Nirenberg inequality. By this argument, a reasonable convergence rate for the zero-dispersion limit is deduced with a slight loss. We also consider the semiclassical limit problem of the Schrödinger-Poisson system in two dimensions.

Original languageEnglish
Article number121502
JournalJournal of Mathematical Physics
Volume56
Issue number12
DOIs
Publication statusPublished - 2015 Dec 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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