Internal stabilization of Navier-Stokes equations with finite-dimensional controllers Viorel BarbuRoberto Triggiani 76D05765535B4035Q30Navier-Stokes equationsstabilizationRiccati equationsteady-state solutionfeedback controller 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. Indiana University Mathematics Journal 2004 text pdf 10.1512/iumj.2004.53.2445 10.1512/iumj.2004.53.2445 en Indiana Univ. Math. J. 53 (2004) 1443 - 1494 state-of-the-art mathematics http://iumj.org/access/