Invariant measures for a stochastic nonlinear Schrodinger equation

被引：43

作者：

Kim, Jong Uhn ^{[1
]}

机构：

[1] Virginia Tech, Dept Math, Blacksburg, VA 24061 USA

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2006年 / 55卷 / 02期

关键词：

Schrodinger equation; Brownian motion; stopping time; Hamiltonian; existence of a solution; invariant measure; probability distribution; tightness;

D O I：

10.1512/iumj.2006.55.2701

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We will prove the existence of an invariant measure for a nonlinear Schrodinger equation with random noise in R-n. The existence of solutions of the Cauchy problem in H-1- and L-2-settings was established by de Bouard and Debussche [4, 5]. Here we discuss only the defocusing equation with a zero-order dissipation. The proof for the existence of an invariant measure is based on various energy estimates and the approximation scheme to construct Solutions, which are also crucial for the existence of global solutions to the Cauchy problem.

引用

页码：687 / 717

页数：31

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