Local martingale solutions to the stochastic one layer shallow water equations

被引：11

作者：

Link, Joshua

Phuong Nguyen ^{[1
]}

Temam, Roger

机构：

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2017年 / 448卷 / 01期

基金：

美国国家科学基金会;

关键词：

Shallow water equations; Stochastic partial differential equations; Galerkin approximation; Martingale solutions; Local existence; PRIMITIVE EQUATIONS; PATHWISE SOLUTIONS; GLOBAL EXISTENCE; CAUCHY-PROBLEM;

D O I：

10.1016/j.jmaa.2016.10.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：93 / 139

页数：47

共 34 条

[1] [Anonymous], 1988, Chicago Lectures in Mathematics
[2] [Anonymous], 1992, ENCY MATH APPL
[3] [Anonymous], 1999, Modern techniques and their applications
[4] [Anonymous], ASPECTS MATH E
[5] STOCHASTIC NAVIER-STOKES EQUATIONS
BENSOUSSAN, A
[J]. ACTA APPLICANDAE MATHEMATICAE, 1995, 38 (03) : 267 - 304
[6] Local solutions for stochastic Navier stokes equations
Bensoussan, A
Frehse, J
[J]. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2000, 34 (02): : 241 - 273
[7] Billingsley P., 1995, WILEY SER PROBAB MAT
[8] ON THE WELL-POSEDNESS FOR THE VISCOUS SHALLOW WATER EQUATIONS
Chen, Qionglei
Miao, Changxing
Zhang, Zhifei
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2008, 40 (02) : 443 - 474
[9] Chow P. L., 2009, COMMUN STOCH ANAL, V2, P211
[10] Explosive solutions of stochastic reaction-diffusion equations in mean Lp-norm
Chow, Pao-Liu
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 250 (05) : 2567 - 2580

← 1 2 3 4 →