Local martingale solutions to the stochastic one layer shallow water equations

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• 作者：Joshua Link ^{josh.link94@gmail.com} ; Phuong Nguyen ; ^{phunguye@umail.iu.edu} ; Roger Temam ^{temam@indiana.edu}
• 关键词：Shallow water equations ; Stochastic partial differential equations ; Galerkin approximation ; Martingale solutions ; Local existence
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 April 2017
• 年：2017
• 卷：448
• 期：1
• 页码：93-139
• 全文大小：700 K
• 卷排序：448

文摘

We consider the single layer shallow water equations on a bounded domain M⊂R2M⊂R2 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 Gyöngy–Krylov theorem, stopping time arguments, and isotropic estimates.