Pullback attractors for a non-autonomous Cahn–Hilliard–Navier–Stokes system in 2D

Article type: Research Article

Authors: Tachim Medjo, T.

Affiliations: Department of Mathematics, Florida International University, DM413B, University Park, Miami, FL 33199, USA. E-mail: tachimt@fiu.edu

Abstract: This article studies the pullback asymptotic behavior of solutions for a non-autonomous Cahn–Hilliard–Navier–Stokes (CH–NS) system in a two-dimensional domain. We prove the existence of pullback attractors 𝒜VM in VM (the velocity has the H1-regularity) and 𝒜YM in YM (the velocity has the L2-regularity). Then we verify the regularity of the pullback attractors by proving that 𝒜VM=𝒜YM, which implies the pullback asymptotic smoothing effect of the model in the sense that the solutions eventually become more regular than the initial data.

Keywords: pullback attractor, non-autonomous two-phase flow, cocycle

DOI: 10.3233/ASY-141225

Journal: Asymptotic Analysis, vol. 90, no. 1-2, pp. 21-51, 2014