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.