Dynamics of the 2D Navier-Stokes equations with sublinear operators in Lipschitz-like domains

Xin-Guang Yang; Rong-Nian Wang; Xingjie Yan; Alain Miranville

doi:10.3934/dcds.2020408

Article Contents

2021, Volume 41, Issue 7: 3343-3366. Doi: 10.3934/dcds.2020408

This issue Previous Article Asymptotic analysis of a structure-preserving integrator for damped Hamiltonian systems Next Article A constructive approach to robust chaos using invariant manifolds and expanding cones

Dynamics of the 2D Navier-Stokes equations with sublinear operators in Lipschitz-like domains

1.
Department of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China
2.
College of Mathematics and Science, Shanghai Normal University, Shanghai, China
3.
Department of Mathematics, China University of Mining and Technology, Xuzhou, 221008, China
4.
Laboratoire de Mathématiques et Applications, Université de Poitiers, UMR CNRS 7348, Site du Futuroscope - Téléport 2
5.
11 Boulevard Marie et Pierre Curie, Bâtiment H3, TSA 61125, 86073 Poitiers Cedex 9, France

^* Corresponding author: Alain Miranville
^* Corresponding author: Alain Miranville

Received: June 2020

Early access: December 2020

Published: July 2021

Research was partly supported by the Fund of Young Backbone Teacher in Henan Province (No. 2018GGJS039)

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Abstract

This paper is concerned with the tempered pullback dynamics of the 2D Navier-Stokes equations with sublinear time delay operators subject to non-homogeneous boundary conditions in Lipschitz-like domains. By virtue of the estimates of background flow in Lipschitz-like domain and a new retarded Gronwall inequality, we establish the existence of pullback attractors in a general setting involving tempered universes.

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Mathematics Subject Classification: 35Q30, 35B40, 35B41, 76D03, 76D05.

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