Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:124

Article

Roeckner, Michael³  Zhu, Rongchan^2,3  Zhu, Xiangchan^1,3 

[1] Beijing Jiaotong Univ, Sch Sci, Beijing 100044, Peoples R China

[2] Beijing Inst Technol, Dept Math, Beijing 100081, Peoples R China

[3] Univ Bielefeld, Dept Math, D-33615 Bielefeld, Germany

关键词: Stochastic fractional partial differential equation;    Local existence and uniqueness;    Blow up;    Navier-Stokes equation;    Fractional Burgers equation;    Quasi-geostrophic equation;    Surface growth models;   

DOI  :  10.1016/j.spa.2014.01.010

来源: Elsevier

【 摘 要 】

In this paper we prove the local existence and uniqueness of solutions for a class of stochastic fractional partial differential equations driven by multiplicative noise. We also establish that for this class of equations adding linear multiplicative noise provides a regularizing effect: the solutions will not blow up with high probability if the initial data is sufficiently small, or if the noise coefficient is sufficiently large. As applications our main results are applied to various types of SPDE such as stochastic reaction diffusion equations, stochastic fractional Burgers equation, stochastic fractional Navier Stokes equation, stochastic quasi-geostrophic equations and stochastic surface growth PDE. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free