Pullback dynamics of 3D Navier-Stokes equations with nonlinear viscosity

Author(s)

Yang, Xin-Guang ^[1] ; Feng, Baowei ^[2] ; Wang, Shubin ^[3] ; Lu, Yongjin ^[4] ; Ma, To Fu ^[5]

Affiliation

^[1] Henan Normal Univ, Dept Math & Informat Sci, Xinxiang 453007 - Peoples R China

^[2] Southwestern Univ Finance & Econ, Coll Econ Math, Chengdu 611130, Sichuan - Peoples R China

^[3] Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan - Peoples R China

^[4] Virginia State Univ, Dept Math & Econ, Petersburg, VA 23806 - USA

^[5] Univ Sao Paulo, Inst Math & Comp Sci, BR-13566590 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS; v. 48, p. 337-361, AUG 2019.
• Web of Science Citations: 2

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. (C) 2019 Elsevier Ltd. All rights reserved. (AU)

• FAPESP's process: 14/17080-0 - Nonautonomous dynamical systems of evolution equations on domains with moving boundary
• Grantee: Xinguang Yang
• Support Opportunities: Scholarships in Brazil - Post-Doctoral