Local and global well-posedness of SPDE with generalized coercivity conditions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:254

Article

Liu, Wei^1,2  Roeckner, Michael^1,3 

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

[2] Jiangsu Normal Univ, Sch Math Sci, Xuzhou 221116, Peoples R China

[3] Purdue Univ, Dept Math & Stat, W Lafayette, IN 47906 USA

关键词: Local monotonicity;    Generalized coercivity;    Navier-Stokes equation;    Surface growth model;    Cahn-Hilliard equation;    Power law fluid;   

DOI  :  10.1016/j.jde.2012.09.014

来源: Elsevier

【 摘 要 】

In this paper we establish the local and global existence and uniqueness of solutions for general nonlinear evolution equations with coefficients satisfying some local monotonicity and generalized coercivity conditions. An analogous result is obtained for stochastic evolution equations in Hilbert space with additive noise. As applications, the main results are applied to obtain simpler proofs in known cases as the stochastic 3D Navier-Stokes equation, the tamed 3D Navier-Stokes equation and the Cahn-Hilliard equation, but also to get new results for stochastic surface growth PDE and stochastic power law fluids. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free