Dynamics of locally monotone stochastic evolution equations

Abstract

This paper is concerned with the dynamics of the locally monotone stochastic evolution equations in Bochner spaces. We first prove the well-posedness of the abstract stochastic evolution equations with locally Lipschitz nonlinear diffusion terms. Then we establish a mean random dynamical system and prove the existence and uniqueness of weak pullback mean random attractors generated by the mean random dynamical system. Furthermore, we prove the existence of invariant measures for the locally monotone model. As applications, the related dynamics for several stochastic models such as stochastic semilinear equations, stochastic Burgers equation and stochastic 2D Navier-Stokes equations are established.