| Abstract: |
| We first consider 3-D Navier Stokes equations whose equilibrium solutions is assumed to be unstable. We then construct explicitly a localized finite dimensional feedback tangential boundary controls such that: if the initial condition is sufficiently close to the equilibrium solution, then the feedback problem is well-posed and uniformly stable. The critical topology is that of a suitable subspace of a Besov space which is close to $ L^3 $. It has the property that it does not recognize compatibility boundary condition while having sufficient smoothness to handle the Navier Stokes non linearity. We shall also present a similar uniform stabilization problem for a Boussinesq system. The role of special unique continuation properties will be emphasized. |
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