Stochastic tamed 3D Navier-Stokes equations: existence, uniqueness and ergodicity

• 成果类型: Article
• 署名作者: Roeckner, Michael; Zhang, Xicheng
• 署名单位: Huazhong University of Science & Technology; University of Bielefeld; Purdue University System; Purdue University; Purdue University System; Purdue University; University of New South Wales Sydney
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-008-0167-5
• 发表日期: 2009
• 页码: 211-267
• 关键词: stationary solutions

摘要

In this paper, we prove the existence of a unique strong solution to a stochastic tamed 3D Navier-Stokes equation in the whole space as well as in the periodic boundary case. Then, we also study the Feller property of solutions, and prove the existence of invariant measures for the corresponding Feller semigroup in the case of periodic conditions. Moreover, in the case of periodic boundary and degenerated additive noise, using the notion of asymptotic strong Feller property proposed by Hairer and Mattingly (Ann. Math. 164:993-1032, 2006), we prove the uniqueness of invariant measures for the corresponding transition semigroup.