The Gromov-Hausdorff Stability For 2D Navier-Stokes Equations

From the Gromov-Hausdorff viewpoint,the aim of this paper is to consider the asymptotic dynamics of 2D Navier-Stokes equations with homogeneous Dirichlet boundary conditions as the region changes.In fact,we mainly prove that the continuous dependence of perturbed semigroups on initial values and perturbed parameters by constructing special ?-immersion.And then,we deduce residual continuity of global attractors and Gromov-Hausdorff stability of 2D Navier-Stokes equations under perturbations of the domain.Besides,we use the properties of the Gromov-Hausdorff convergence to study the geometric structure of the global attractors.