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This work is concerned about the asymptotic behavior of the solutions of thetwo and three dimensional stochastic convective Brinkman-Forchheimer (SCBF)equations driven by white noise with nonlinear diffusion terms. We prove theexistence and uniqueness of weak pullback mean random attractors for the 2DSCBF 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 thediffusion terms are Lipschitz nonlinear functions. Furthermore, we establishthe existence of weak pullback mean random attractors for a class of locallymonotone stochastic partial differential equations.

infinite dimensional analysis quantum probability and related topics

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