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) equations [Formula: see text] [Formula: see text] driven by white noise with nonlinear diffusion terms (for some [Formula: see text]). We prove the existence and uniqueness of weak pullback mean random attractors for the 2D SCBF equations (for [Formula: see text]) as well as 3D SCBF equations (for [Formula: see text], any [Formula: see text] and for [Formula: see text], [Formula: see text]) 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.