Stochastic 2-D Navier-Stokes equation

被引：116

作者：

Menaldi, JL ^{[1
]}

Sritharan, SS

机构：

[1] Wayne State Univ, Dept Math, Detroit, MI 48202 USA

[2] USN, SPAWAR SSD, San Diego, CA 92152 USA

来源：

APPLIED MATHEMATICS AND OPTIMIZATION | 2002年 / 46卷 / 01期

关键词：

stochastic Navier-Stokes equation; maximal monotone operator; Markov-Feller semigroup; stochastic differential equations;

D O I：

10.1007/s00245-002-0734-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this significantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier-Stokes martingale problem where the probability space is also obtained as a part of the solution.

引用

页码：31 / 53

页数：23

共 23 条

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