Local solvability of free boundary problem for viscous compressible and incompressible fluids in the spaces $W_p^{2+l,1+l/2}(Q_T)$, $p>2$

We prove local in time solvability of the free boundary problem for two phase viscous compressible and incompressible fluids in the spaces $W_p^{2+l,1+l/2}(Q_T)$ with $p>2$, $l\in(1/p,2/p)$.