Local martingale solutions to the stochastic two layer shallow water equations with multiplicative white noise

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:461

Article

Phuong Nguyen¹ 

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

关键词: Martingale solutions;    Pathwise solutions;    Galerkin approximation scheme;    Stochastic partial differential equations;   

DOI  :  10.1016/j.jmaa.2017.10.045

来源: Elsevier

【 摘 要 】

We study the two layers shallow water equations on a bounded domain M subset of R-2 driven by a multiplicative white noise, and obtain the existence and uniqueness of a maximal pathwise solution for a limited period of time, the time of existence being strictly positive almost surely. The proof makes use of anisotropic estimates and stopping time arguments, of the Skorohod representation theorem, and the Gyongy-Krylov theorem which is an infinite dimensional analogue of the Yamada-Watanabe theorem. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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