STABILIZATION OF THE NON-HOMOGENEOUS NAVIER-STOKES EQUATIONS IN A 2D CHANNEL
Résumé
In this article we study the local boundary stabilization of the non-homogeneous Navier-Stokes equations in a 2d channel around Poiseuille flow which is a stationary solution for the system under consideration. The feedback control operator we construct has finite dimensional range. The homogeneous Navier-Stokes equations are of parabolic nature and the stabilization result for such system is well studied in the literature. In the present article we prove a stabilization result for non-homogeneous Navier-Stokes equations which involves coupled parabolic and hyperbolic dynamics by using only one boundary control for the parabolic part.
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