Martingale solutions and Markov selections for stochastic partial differential equations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Goldys, Benjamin²  Roeckner, Michael^1,3  Zhang, Xicheng^1,2,4 

[1] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany

[2] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

[3] Purdue Univ, Dept Math & Stat, W Lafayette, IN 47907 USA

[4] Huazhong Univ Sci & Technol, Dept Math, Wuhan 430074, Peoples R China

关键词: Markov selection;    Martingale solution;    Stochastic porous medium equation;    Stochastic Navier-Stokes equation;   

DOI  :  10.1016/j.spa.2008.08.009

来源: Elsevier

【 摘 要 】

We present a general framework for solving stochastic porous medium equations and stochastic Navier-Stokes equations in the sense of martingale solutions. Following Krylov [N.V. Krylov, The selection of a Markov process from a Markov system of processes, and the construction of quasidiffusion processes, Izv. Akad. Nauk SSSR Ser. Mat. 37 (1973) 691-708] and Flandoli-Romito [F. Flandoli, N. Romito, Markov selections for the 3D stochastic Navier-Stokes equations, Probab. Theory Related Fields 140 (2008) 407-458], we also study the existence of Markov selections for stochastic evolution equations in the absence of uniqueness. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

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