On local $L_p$-$L_q$ well-posedness of incompressible two-phase flows with phase transitions: the case of non equal densities

Abstract

The basic model for incompressible two-phase flows with phase transitions where the interface is nearly flat in the case of non-equal densities is considered. The local well-posedness of the model in $L_p$-setting was proved in Prüss and Shimizu [14]. In this paper, we prove local well-posedness of the model $L_p$ in time $L_q$ in space settting.