Pullback attractors for 2D Navier–Stokes equations on time-varying domains. (February 2019)

• Record Type: Journal Article
• Authors: Song, Xiaoya; Sun, Chunyou; Yang, Lu
• Is Part Of: Nonlinear analysis. Volume 45(2019)
• Page Start: 437
• Page End: 460
• Publication Date: 2019-02
• Subjects: 2D Navier–Stokes equations -- Time-varying domain -- Pullback attractor; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.07.013
• Languages: English
• ISSNs: 1468-1218

Abstract

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.