DISPERSIVE LIMIT OF THE EULER-POISSON SYSTEM IN HIGHER DIMENSIONS

被引：32

作者：

Pu, Xueke ^{[1
,2
]}

机构：

[1] Chongqing Univ, Dept Math, Chongqing, Peoples R China

[2] Math Sci Res Inst, Chongqing, Peoples R China

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2013年 / 45卷 / 02期

关键词：

Euler-Poisson equation; Kadomtsev-Petviashvili II equation; Zakharov-Kuznetsov equation; long wavelength limit; KP-II EQUATION; CRITICAL THRESHOLDS; WELL-POSEDNESS; CAUCHY-PROBLEM;

D O I：

10.1137/120875648

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the dispersive limit of the Euler-Poisson system for ion-acoustic waves. We establish that under the Gardner-Morikawa type transformations, the solutions of the Euler-Poisson system converge globally to the Kadomtsev Petviashvili II (KP-II) equation in R-2 and the Zakharov-Kuznetsov equation (ZKE) in R-3 for well-prepared initial data, under different scalings. This justifies rigorously the KP-II limit and the ZKE limit of the Euler-Poisson equation.

引用

页码：834 / 878

页数：45

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