On the stabilization of a hyperbolic Stokes system under geometric control condition

TL;DR

This paper proves exponential stabilization of a hyperbolic Stokes system on a bounded domain when damping is applied in a geometrically controlled subdomain, using a new quasi-mode estimate.

Contribution

It introduces a novel quasi-mode estimate that enables exponential decay results for the hyperbolic Stokes system under geometric control conditions.

Findings

System decays exponentially with damping in the controlled subdomain

New quasi-mode estimate for the Stokes system

Exponential stabilization achieved under geometric control condition

Abstract

In this paper, we study the stabilization problem for a hyperbolic type Stokes system posed on a bounded domain. We show that when the damping effects are restricted to a subdomain satisfying the geometrical control condition the system decays exponentially. The result is a consequence of a new quasi-mode estimate for the Stokes system.