Null Controllability of One-Dimensional Linearized Compressible Navier-Stokes System in Periodic Setup Using One Boundary Control

Jiten Kumbhakar

Published 2023-01-10Version 1

In this article, we study boundary null controllability properties of the linearized compressible Navier-Stokes equations in one dimension for both barotropic and non-barotropic fluids using only one boundary control. The control acts through periodic boundary conditions. We prove null controllability of the linearized compressible Navier-Stokes system (for both barotropic and non-barotropic fluids) at large time $T$. We also prove that our result is sharp with respect to the regularity of the initial states. Finally, for both barotropic and non-barotropic fluids, we prove a lack of controllability at small time $T$ when a control acts in density.