The dimension of attractor of the 2D g-Navier–Stokes equations

Abstract: The g-Navier–Stokes equations in spatial dimension 2 were introduced by Roh as with the continuity equation where g is a suitable smooth real valued function. Roh proved the existence of global solutions and the global attractor, for the spatial periodic and Dirichlet boundary conditions. Roh also proved that the global attractor of the g-Navier–Stokes equations converges (in the sense of upper continuity) to the global attractor of the Navier–Stokes equations as in the proper sense. In this paper, we will estimate the dimension of the global attractor , for the spatial periodic and Dirichlet boundary conditions. Then, we will see that the upper bounds for the dimension of the global attractors converge to the corresponding upper bounds for the global attractor as in the proper sense. [Copyright &y& Elsevier]