The g-Navier-Stokes equations in spatial dimension 2 were introduced by Roh aswith the continuity equationwhere 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 A g of the g-Navier-Stokes equations converges (in the sense of upper continuity) to the global attractor A 1 of the Navier-Stokes equations as g → 1 in the proper sense.In this paper, we will estimate the dimension of the global attractor A g , for the spatial periodic and Dirichlet boundary conditions. Then, we will see that the upper bounds for the dimension of 437 the global attractors A g converge to the corresponding upper bounds for the global attractor A 1 as g → 1 in the proper sense. 2005 Elsevier Inc. All rights reserved.
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