Regularity of uniform attractor for 3D non-autonomous Navier-Stokes-Voigt equation.

In this paper, we study the large time behavior for 3D viscoelastic incompressible fluid flow subject to Kelvin–Voigt damping and a time varying external force. The evolution of the dynamic is governed by a 3D non-autonomous Navier–Stokes–Voigt (NSV) equation. We assume that the external force is in the space of translation bounded functions (or its sub-spaces) that requires less compactness than the space of translation compact functions. We formulate the system in the framework of skew product flow. By defining an appropriate energy space that incorporates the Kelvin–Voigt damping, we established the existence of regular strong uniform attractor for the NSV equation in energy space W˜ and provide a description of the general structure of the uniform attractor. Our result improves the H01 regularity of global attractor of the system under study.