Gromov-Hausdorff stability of global attractors for the 3D incompressible Navier-Stokes-Voigt equations

Abstract

The structure stability from the Gromov-Hausdorff viewpoint can be used to describe the continuity of complete trajectories inside global attractors for nonlinear evolutionary partial differential equations defined on perturbed domains, such as the unsteady incompressible fluid flow models. This paper is concerned with the Gromov-Hausdorff stability for the three dimensional Navier-Stokes-Voigt equations by combining the properties of the inverse operator associated with the Laplacian to deal with transformations of different domains to avoid higher regularity estimates. The key technique lies in the construction of new equations on perturbed domains and the normalized method to obtain the compactness.