Communications in Mathematical Sciences

Volume 13 (2015)

Number 1

Global well-posedness of stochastic Burgers system

Pages: 153 – 169

DOI: https://dx.doi.org/10.4310/CMS.2015.v13.n1.a8

Authors

Boling Guo (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Yongqian Han (Institute of Applied Physics and Computational Mathematics, Beijing, China)

Guoli Zhou (Chong Qing University, Beijing, China; Institute of Applied Physics and Computational Mathematics, Beijing, China)

Abstract

In this paper a stochastic Burgers system in Itô form is considered. The global well-posedness is proved. The proof relies on energy estimates for the velocity. A maximum principle of deterministic parabolic equations is used to overcome the difficulties arising from higher order norms. The methods and results can be applied to other parabolic equations with additive white noise such as stochastic reaction diffusion equations.

Keywords

stochastic Burgers system, Wiener noise, global solution

2010 Mathematics Subject Classification

60H15, 76S05

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Published 16 July 2014