## Differential and Integral Equations

### 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.

#### Article information

Source
Differential Integral Equations, Volume 28, Number 1/2 (2015), 29-58.

Dates
First available in Project Euclid: 11 December 2014

Shimizu, Senjoi; Yagi, Shintaro. On local $L_p$-$L_q$ well-posedness of incompressible two-phase flows with phase transitions: the case of non equal densities. Differential Integral Equations 28 (2015), no. 1/2, 29--58. https://projecteuclid.org/euclid.die/1418310420