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

Abstract

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 \begin{document} $H_0^1\cap H^2$ \end{document} 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.