In this talk we show that by stabilizing a steady state solution to the Galerkin approximation of the Navier-Stokes equations, using certain linear feedback control, one in fact is stabilizing a nearby steady state solution to the fully three dimensional Navier-Stokes equations. Similar results also hold in the context of Nonlinear Galerkin method. It is worth mentioning that all our conditions are explicit and verified by the computed approximate Galerkin solution and that no a priori assumptions are made on the unknown exact solution of the Navier-Stokes equations.

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