# American Institute of Mathematical Sciences

January  2019, 24(1): 363-386. doi: 10.3934/dcdsb.2018084

## Long-time dynamics for a non-autonomous Navier-Stokes-Voigt equation in Lipschitz domains

 1 College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China 2 College of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, China 3 Instituto de Ciências Matemáticas e da Computação, Universidade de São Paulo-Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos SP, Brazil 4 Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA 5 Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, IN 46556, USA

* Corresponding author: Taige Wang

Received  October 2016 Revised  August 2017 Published  March 2018

Fund Project: Xinguang Yang is supported by FAPESP, Grant 2014/17080-0, the Mainstay Fund from Henan Normal University, the Program for Science and Technology Innovation Talents in University of Henan Province (No. 142102210448); Baowei Feng is supported by National Natural Foundation of China (No. 11701465)

This article focuses on the optimal regularity and long-time dynamics of solutions of a Navier-Stoke-Voigt equation with non-autonomous body forces in non-smooth domains. Optimal regularity is considered, since the regularity $H_0^1\cap H^2$ cannot be achieved. Given the initial data in certain spaces, it can be shown that the problem generates a well-defined evolutionary process. Then we prove the existence of a uniform attractor consisting of complete trajectories.

Citation: Xinguang Yang, Baowei Feng, Thales Maier de Souza, Taige Wang. Long-time dynamics for a non-autonomous Navier-Stokes-Voigt equation in Lipschitz domains. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 363-386. doi: 10.3934/dcdsb.2018084
##### References:
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##### References:
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