STABILIZATION OF THE NON-HOMOGENEOUS NAVIER-STOKES EQUATIONS IN A 2D CHANNEL

Sourav Mitra (1, 2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 UT3 - Université Toulouse III - Paul Sabatier

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.

Mots clés: Non-homogeneous Navier-Stokes equations; inflow boundary control; feedback law

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Sourav Mitra. STABILIZATION OF THE NON-HOMOGENEOUS NAVIER-STOKES EQUATIONS IN A 2D CHANNEL. 2018. ⟨hal-01959687⟩