# American Institute of Mathematical Sciences

July  2021, 41(7): 3343-3366. doi: 10.3934/dcds.2020408

## 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

Received  June 2020 Published  December 2020

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

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.

Citation: Xin-Guang Yang, Rong-Nian Wang, Xingjie Yan, Alain Miranville. Dynamics of the 2D Navier-Stokes equations with sublinear operators in Lipschitz-like domains. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3343-3366. doi: 10.3934/dcds.2020408
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