# Null controllability of Compressible Navier-Stokes system in one dimension

Interior local null controllability of one-dimensional compressible Navier-Stokes equations with periodic boundary conditions, with initial conditions in a small neighbourhood of a state of uniform density and uniform nonzero velocity is analysed. We prove that, with a control given by a body force localized in a subinterval, we can steer the system to uniform density and velocity. The novelty is that only one control for velocity is shown to be enough to control both density and velocity.

**People**: Debanjana Mitra, Mythily Ramaswamy and Michael Renardy

**Status**: Paper submitted