Abstract

In this paper, we study the boundary controllability of the compressible Navier--Stokes equations on a bounded domain $\Omega$ in the nonisentropic case with a control on the whole boundary. We prove local controllability around a constant state with nonzero velocity in dimensions 1, 2, and 3. The main idea of the proof is to use a fixed point argument in adequate Sobolev spaces with Carleman weights that relies on the controllability of the linearized system, which in turn uses another fixed point using the controllability of the decoupled systems.