Null controllability of the linearized compressible Navier–Stokes equations using moment method

Abstract

In this paper, we consider one-dimensional compressible Navier–Stokes equations linearized around a constant steady state (Q0, V0), Q0 > 0, V0 > 0 with periodic boundary condition. We explore the controllability of this linearized system using a control only for the velocity equation. We establish that the linearized system with periodic boundary conditions is null controllable when time is large enough, for regular initial data by a localized interior control. Finally, we show that this system is boundary null controllable, when time is large enough, for slightly less regular initial data compared to interior controllability case.