Exact boundary controllability of Galerkin approximations of Navier-Stokes system for soret convection

Abstract

We study the exact controllability of finite dimensional Galerkin approximation of a NavierStokes type system describing doubly diffusive convection with Soret effect in a bounded smooth domainin Rd(d = 2, 3) with controls on the boundary. The doubly diffusive convection system with Soret effectinvolves a difficult coupling through second order terms. The Galerkin approximations are introducedunder certain assumptions on the Galerkin basis related to the linear independence of suitable tracesof its elements over the boundary. By Using Hilbert uniqueness method in combination with a fixedpoint argument, we prove that the finite dimensional Galerkin approximations are exactly controllable.