Local martingale solutions to the stochastic one layer shallow water equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:448

Article

Phuong Nguyen¹ 

[1] Indiana Univ, Dept Math, Bloomington, IN 47405 USA

关键词: Shallow water equations;    Stochastic partial differential equations;    Galerkin approximation;    Martingale solutions;    Local existence;   

DOI  :  10.1016/j.jmaa.2016.10.036

来源: Elsevier

【 摘 要 】

We consider the single layer shallow water equations on a bounded domain M subset of R-2 forced by a multiplicative white noise, and obtain the existence and uniqueness of a maximal pathwise solution for a short period of time. The proof relies on the Skorohod representation theorem, the Gyongy Krylov theorem, stopping time arguments, and isotropic estimates. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free