An optimal control problem for two-phase compressible-incompressible flows

In this work two-phase compressible-incompressible flows are studied. In particular, the possibility of driving the gas bubbles moving in a liquid towards a prescribed position is investigated. To this end, first a well-established mathematical model for two-phase compressible-incompressible fluids is briefly introduced, then an adjoint-based optimal control problem is defined. Finally numerical results on the controllability of the system are presented.