Exact Local Controllability of a Two-Dimensional Viscous Gas Flow

Abstract

In a two-dimensional bounded domain $$\Omega $$ , we consider the system of Navier–Stokes equations describing the flow of a viscous compressible gas with no allowance for heat exchange with the ambient medium under small variations of density in the equations of motion. We prove the existence of a solution to the problem of exact local controllability of this system by an external force supported in an arbitrary fixed subdomain $$\omega \subset \Omega $$ .