Weak pullback mean random attractors for the stochastic convective Brinkman-Forchheimer equations and locally monotone stochastic partial differential equations

TL;DR

This paper investigates the long-term behavior of solutions to stochastic convective Brinkman-Forchheimer equations and related SPDEs, establishing the existence and uniqueness of weak pullback mean random attractors under certain conditions.

Contribution

It proves the existence and uniqueness of weak pullback mean random attractors for 2D and 3D stochastic convective Brinkman-Forchheimer equations with Lipschitz diffusion terms, extending to locally monotone SPDEs.

Findings

Existence and uniqueness of weak pullback mean random attractors for 2D SCBF equations.

Existence of attractors for 3D SCBF equations under specific parameter conditions.

Extension of attractor results to a class of locally monotone SPDEs.

Abstract

This work is concerned about the asymptotic behavior of the solutions of the two and three dimensional stochastic convective Brinkman-Forchheimer (SCBF) equations driven by white noise with nonlinear diffusion terms. We prove the existence and uniqueness of weak pullback mean random attractors for the 2D SCBF equations (for $r\geq1$) as well as 3D SCBF equations (for $r>3$, any $\mu,\beta>0$ and for $r=3$, $2\mu\beta\geq1$) in Bochner spaces, when the diffusion terms are Lipschitz nonlinear functions. Furthermore, we establish the existence of weak pullback mean random attractors for a class of locally monotone stochastic partial differential equations.