Pullback attractors for 2D MHD equations with delays

Abstract

The aim of this paper is to consider the asymptotic dynamics of solutions to 2D MHD equations when the external forces contain some hereditary characteristics. First, we establish, respectively, the well-posedness of strong solutions and weak solutions; then, the process $\tilde{U}(\cdot ,\cdot )$ generated by the weak solutions is constructed in $M_H^2(=H\times L_H^2)$ ; and finally, we analyze the long-time behavior of the weak solutions by proving the existence of a compact pullback attractor.