Interior local null controllability for multi-dimensional compressible flow near a constant state

Abstract

We consider compressible flow with periodic boundary conditions. In a neighborhood of a state of constant density and nonzero velocity, we prove exact null controllability of the system with a control localized in space and acting only on the momentum equation.

Lack of null controllability of one dimensional linear coupled transport-parabolic system with variable coefficients

“…In the context of compressible Navier-Stokes systems, the local exact controllability around constant states was studied in [10,9,24,23,25], and an analogous result around variable trajectories was obtained in [11].…”