Invariant measures for stochastic 3D Lagrangian-averaged Navier–Stokes equations with infinite delay
发布时间：2022-12-08
点击次数：
- 论文编号：
- 107004
- 第一作者：
- 杨爽
- 发表刊物：
- Communications in Nonlinear Science and Numerical Simulation
- 收录刊物：
- SCI
- 刊物所在地：
- NETHERLANDS
- 文献类型：
- J
- 卷号：
- 118
- 关键字：
- Stochastic 3D Lagrangian-averaged Navier-Stokes equations; Infinite delay; Random attractors; Invariant measures; Generalized Banach limit
- DOI码：
- 10.1016/j.cnsns.2022.107004
- 摘要：
- In this paper we investigate stochastic dynamics and invariant measures for stochastic 3D Lagrangian-averaged Navier-Stokes (LANS) equations driven by infinite delay and additive noise. We first use Galerkin approximations, a priori estimates and the standard Gronwall lemma to show the well-posedness for the corresponding random equation, whose solution operators generate a random dynamical system. Next, the asymptotic compactness for the random dynamical system is established via the Ascoli-Arzelà theorem. Besides, we derive the existence of a global random attractor for the random dynamical system. Moreover, we prove that the random dynamical system is bounded and continuous with respect to the initial values. Eventually, we construct a family of invariant Borel probability measures, which is supported by the global random attractor.