Pullback attractors for 2D Navier–Stokes equations on time-varying domains. (February 2019) - Song, Xiaoya; Sun, Chunyou; Yang, Lu
Abstract: The aim of this paper is to consider the asymptotic dynamics of 2D Navier–Stokes equations on the time-varying domains with homogeneous Dirichlet boundary conditions. First, we establish the existence and uniqueness of weak solutions, it is assumed that the spatial domains O t in R 2 are obtained from a bounded base domain O by a C 3 -diffeomorphism r ( ⋅, t ) ; then, some useful equivalent estimates about the vectors on time-varying domains and cylindrical domains are given; and finally, we analyze the long-time behavior of the solutions by proving the existence of a pullback compact attractor.