Local solvability of free boundary problem for viscous compressible and incompressible fluids in the spaces \({W}_p^{2+l,1+l/2} (Q_T)\), \(p > 2\) (Q2667853)

The author studies solvability of evolutionary free boundary problem for two phase viscous fluids of different types. The unknown domain is in \(\mathbb{R}^3\), with classical boundary conditions, including non-permeable walls, continuity of velocity at the free boundary, and the boundary itself defined as separation surface between two fluids. The authors proves existence and uniqueness of a solution locally in time in the space \(W_p^{2+l,1+l/2}\).