This paper is concerned with the basic model for compressible and incompressible two phase flows with phase transitions The flows are separated by nearly flat interface represented as a graph over the $N-1$ dimensional Euclidean space ${ \Bbb R}^{ N-1}$ ($N \geq 2$). The local well-posedness is proved by the Banach fixed point theorem based on the maximal $L_p$-$L_q$ regularity theorm for the linearized problem.
Categories: math.AP