Document Code:

107004

First Author:

Shuang Yang

Journal:

Communications in Nonlinear Science and Numerical Simulation

Included Journals:

SCI

Place of Publication:

NETHERLANDS

Document Type:

J

Volume:

118

Key Words:

Stochastic 3D Lagrangian-averaged Navier-Stokes equations; Infinite delay; Random attractors; Invariant measures; Generalized Banach limit

DOI number:

10.1016/j.cnsns.2022.107004

Abstract:

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.

Links to published journals:

https://www.sciencedirect.com/science/article/pii/S1007570422004919?dgcid=author