Pullback dynamics of 3D Navier–Stokes equations with nonlinear viscosity. (August 2019)

• Record Type: Journal Article
• Authors: Yang, Xin-Guang; Feng, Baowei; Wang, Shubin; Lu, Yongjin; Ma, To Fu
• Is Part Of: Nonlinear analysis. Volume 48(2019)
• Page Start: 337
• Page End: 361
• Publication Date: 2019-08
• Subjects: Navier–Stokes equations -- Nonlinear viscosity -- Pullback attractors -- Fractal dimension -- Ladyzhenskaya model; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.01.013
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper is concerned with pullback dynamics of 3D Navier–Stokes equations with variable viscosity and subject to time-dependent external forces. Our main result establishes the existence of finite-dimensional pullback attractors in a general setting involving tempered universes. We also present a sufficient condition on the viscosity coefficients that guarantees the attractors are nontrivial. We end the paper by showing the upper semi-continuity of pullback attractors as the non-autonomous perturbation vanishes.