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

Satoshi Masaki, Takayoshi Ogawa

研究成果: Article査読

抄録

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.

本文言語English
論文番号121502
ジャーナルJournal of Mathematical Physics
56
12
DOI
出版ステータスPublished - 2015 12月 1

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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