Abstract
We discuss here the nonlinear Galerkin method which corresponds to the projection of the equations under consideration on a nonlinear manifold close to the attractor. This method stems from the theory of inertial manifolds and approximate inertial manifolds which has proved to be a powerful tool of investigation for dynamical systems. We intend to briefly review some results concerning the attractors for the Navier-Stokes equations and their approximations
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