Approximate controllability for linearized compressible barotropic Navier-Stokes system in one and two dimensions

In this paper we consider compressible barotropic Navier-Stokes equations in one and two dimensions linearized around a constant steady state with Dirichlet boundary conditions. We explore the controllability of this linearized system using a control only for the velocity equation. We prove that the system with homogeneous Dirichlet boundary conditions, is approximately controllable by a localized interior control when time is sufficiently large.