Stabilization of the non-homogeneous Navier–Stokes equations in a 2d channel

Author:

Mitra Sourav

Abstract

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.

Publisher

EDP Sciences

Subject

Computational Mathematics,Control and Optimization,Control and Systems Engineering

Reference41 articles.

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2. Stabilization of Parabolic Nonlinear Systems with Finite Dimensional Feedback or Dynamical Controllers: Application to the Navier–Stokes System

3. Local controllability to trajectories for non-homogeneous incompressible Navier–Stokes equations

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