Local exact controllability for a viscous compressible two-phase model

Abstract This paper is devoted to the boundary controllability of a viscous compressible two-phase system modeling the motion of the mixture of fluid and particles. Based on the observability inequality of the adjoint system of a new linearized system including the equation of the pressure and the fixed point argument, the local exact controllability of this system on a constant target trajectory is obtained. The initial density of the fluid and the particles may contain vacuum and one of the target density allows to be vanish.