IUMJ

Title: Internal stabilization of Navier-Stokes equations with finite-dimensional controllers

Authors: Viorel Barbu and Roberto Triggiani

Issue: Volume 53 (2004), Issue 5, 1443-1494

Abstract:

The steady-state solutions to Navier-Stokes equations on $\Omega \subset \mathbb{R}^d$, $d=2$, $3$, with no-slip boundary conditions, are locally exponentially stabilizable by a finite-dimensional feedback controller with support in an arbitrary open subset $\omega \subset \Omega$ of positive measure. The (finite) dimension of the feedback controller is related to the largest algebraic multiplicity of the unstable eigenvalues of the linearized equation.