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

Abstract

This work is concerned about the asymptotic behavior of the solutions of the two and three dimensional stochastic convective Brinkman-Forchheimer (SCBF) equationsdriven by white noise with nonlinear diffusion terms (for some ε > 0). We prove the existence and uniqueness of weak pullback mean random attractors for the 2D SCBF equations (for r ≥ 1) as well as 3D SCBF equations (for r > 3, any µ, β > 0 and for r = 3, 2µβ ≥ 1) 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.