#### Alladi Ramakrishnan Hall

#### Null controllability of the linearized compressible Navier-Stokes system in one dimension

#### Michael Renardy

##### Virginia Tech, USA

*We consider the one dimensional compressible Navier-Stokes equations*

linearized around constant density and velocity, with periodic boundary

conditions. For nonzero velocity, we prove null controllability of this

linearized system using a control only for the velocity equation.

The proof is based on a splitting of parabolic and hyperbolic parts of the

equation and on two types of Ingham inequalities.

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.

This is joint work with Shirshendu Chowdhury, Debanjana Mitra and Mythily

Ramaswamy.

Done