Stabilization of the non-homogeneous Navier–Stokes equations in a 2d channel
ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 66.

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.

DOI : 10.1051/cocv/2019036
Classification : 35K55, 76D05, 76D55, 93D15, 93D30
Mots-clés : Non-homogeneous Navier–Stokes equations, inflow boundary control, feedback law
Mitra, Sourav 1

1 
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Mitra, Sourav. Stabilization of the non-homogeneous Navier–Stokes equations in a 2d channel. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 66. doi : 10.1051/cocv/2019036. http://www.numdam.org/articles/10.1051/cocv/2019036/

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