The Estimation of the Hausdorff and Fractal Dimensions of the Global Attractor for 2D Autonomous g-Navier-Stokes Equations

Abstract

In this paper, by using the energyequation method, the 2D g-Navier-Stokes equations with linear dampness on some unbounded domains wereinvestigated without the restriction of the forcing term belongingto some weighted Sobolev space. Moreover,the estimation of theHausdorff and Fractal dimensions of such attractors were alsoobtained.

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

“…Recently, the asymptotic determination and reduction of the 2D incompressible Navier-Stokes equations in Lipschitz domains have been studied in [49]. The Gromov-Hausdorff stability of reduced functional equations based on the asymptotic determination for evolutionary dissipative systems is another aspect for the structure stability related to dynamical systems on perturbed domains, especially for to the 2D Navier-Stokes fluid flow, see [47]. The Gromov-Hausdorff stability of three dimensional fluid flow models can be used to describe geometric properties of perturbations, which is also a hot issue in hydrodynamics.…”