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

被引：58
|
作者：
Roeckner, Michael [2 ,3 ,4 ]
Zhang, Xicheng [1 ,2 ,5 ]
机构：
[1] Huazhong Univ Sci & Technol, Dept Mech, Wuhan 430074, Peoples R China
[2] Univ Bielefeld, Fak Math, D-33501 Bielefeld, Germany
[3] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA
[4] Purdue Univ, Dept Stat, W Lafayette, IN 47907 USA
[5] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia
来源：
PROBABILITY THEORY AND RELATED FIELDS | 2009年 / 145卷 / 1-2期
关键词：
Navier-Stokes equation; Invariant measure; Ergodicity; Asymptotic strong Feller property; STATIONARY SOLUTIONS;
D O I：
10.1007/s00440-008-0167-5
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
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.
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页码：211 / 267
页数：57
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