Pullback attractors for a non-autonomous homogeneous two-phase flow model

Abstract

This article studies the pullback asymptotic behavior of solutions for a non-autonomous homogeneous two-phase flow model in a two-dimensional domain. We prove the existence of pullback attractors AV in V (the velocity has the H1-regularity) and AY in Y (the velocity has the L2-regularity). Then we verify the regularity of the pullback attractors by proving that AV=AY, which implies the pullback asymptotic smoothing effect of the model in the sense that the solutions eventually become more regular than the initial data. The method used in this article is similar to the one used in Zhao and Zhou (2007) [42] in the case of the non-autonomous incompressible non-Newtonian fluid in a two-dimensional domain. Let us mention that the nonlinearity involved in the model considered in this article is stronger than the one in the two-dimensional non-Newtonian flow studied in Zhao and Zhou (2007) [42].