On approximate Inertial Manifolds to the Navier-Stokes equations
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Recently, the theory of Inertial Manifolds has shown that the long time behavior (the dynamics) of certain dissipative partial differential equations can be fully discribed by that of a finite ordinary differential system. Although we are still unable to prove existence of Inertial Manifolds to the Navier-Stokes equations, we present here a nonlinear finite dimensional analytic manifold that approximates closely the global attractor in the two-dimensional case, and certain bounded invariant sets in the three-dimensional case. This approximate manifold and others allow us to introduce modified Galerkin approximations. © 1990.
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