On the $\mathcal R$-Boundedness for the Two Phase Problem with Phase Transition: Compressible-Incompressible Model Problem

抄録

In this paper, we prove the maximal L_p-L_q regularity of the compressible and incompressible two phase flow with phase transition in the model problem case with the help of $\mathcal R$-bounded solution operators corresponding to generalized resolvent problem. The problem arises from the mathematical study of the motion of two-phase flows having gaseous phase and liquid phase separated by a sharp interface with phase transition.