Existence and Nonlinear Stability of Stationary States for the Semi-Relativistic Schrödinger-Poisson System

被引：0
|
作者：
Walid Abou Salem
Thomas Chen
Vitali Vougalter
机构：
[1] University of Saskatchewan,Department of Mathematics and Statistics
[2] University of Texas at Austin,Department of Mathematics
[3] University of Cape Town,Department of Mathematics and Applied Mathematics
[4] Private Bag,undefined
来源：
Annales Henri Poincaré | 2014年 / 15卷
关键词：
Stationary State; Sobolev Inequality; Mild Solution; Nonlinear Stability; Unique Maximizer;
D O I：
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中图分类号：
学科分类号：
摘要：
We study the stationary states of the semi-relativistic Schrödinger-Poisson system in the repulsive (plasma physics) Coulomb case. In particular, we establish the existence and the nonlinear stability of a wide class of stationary states by means of the energy-Casimir method. We generalize the global well-posedness result of (Abou Salem et al. in Dyn Partial Differ Equ 9(2):121–132, 2012) for the semi-relativistic Schrödinger-Poisson system to spaces with higher regularity.
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页码：1171 / 1196
页数：25
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