Michael Renardy
MATHEMATICS COLLOQUIUM
Speaker: Michael Renardy Abstract. We consider the one dimensional compressible Navier-Stokes equations linearized around a steady state of constant density and constant nonzero velocity, with periodic boundary conditions. We explore the controllability of this linearized system using a control only for the velocity equation. We prove that the linearized system with homogeneous periodic boundary conditions is null controllable in an appropriate Sobolev space by a localized interior control when time is sufficiently large. The proof is based on an observability inequality obtained with the help of two types of Ingham inequality. p> We also consider the analogous problem with Dirichlet boundary conditions rather than periodicity. For this case, we show approximate controllability and null controllability in the case of creeping flow. |