Upper Semicontinuity of Strong Pullback Attractors for Delay Non-autonomous Dynamical Systems and Application to Double Time-delayed 2D MHD Equations

Abstract

The long term behavior of delay-dependent evolution processes generated by delay partial differential equations with non-autonomous forcing terms is analysed. First, we introduce some concepts on strong pullback attractors. We then establish a general theory concerning the existence of such attractors for abstract delay models. Moreover, we investigate the upper semicontinuity of strong pullback attractors in the regular space as the delay time tends to zero. Eventually, we apply the general results to double time-delayed 2D magnetohydrodynamics (MHD) equations. Since their solutions have no high regularity, we prove the strong pullback asymptotic compactness of solution operators via the flattening of solutions.

Keywords

Strong pullback attractor / upper semicontinuity / delay / MHD equations