Volume 25, 2019
|Number of page(s)||35|
|Published online||01 November 2019|
Stabilization of the non-homogeneous Navier–Stokes equations in a 2d channel
Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS IMT,
Toulouse Cedex 9, France.
* Corresponding author: Sourav.Mitra@math.univ-toulouse.fr
Accepted: 12 May 2019
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.
Mathematics Subject Classification: 35K55 / 76D05 / 76D55 / 93D15 / 93D30
Key words: Non-homogeneous Navier–Stokes equations / inflow boundary control / feedback law
© The author. Published by EDP Sciences, SMAI 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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