## Advances in Differential Equations

### On local $L_p$-$L_q$ well-posedness of incompressible two-phase flows with phase transitions: Non-equal densities with large initial data

#### Abstract

A 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. Local well-posedness of the model in $L_p$ in a time setting $L_q$ in a space setting was proved in [30] under a smallness assumption for the initial data. In this paper, we remove the smallness assumption for the initial data.

#### Article information

Source
Adv. Differential Equations, Volume 22, Number 9/10 (2017), 737-764.

Dates
First available in Project Euclid: 27 May 2017

Permanent link to this document
https://projecteuclid.org/euclid.ade/1495850458

Mathematical Reviews number (MathSciNet)
MR3656491

Zentralblatt MATH identifier
06780898

#### Citation

Shimizu, Senjo; Yagi, Shintaro. On local $L_p$-$L_q$ well-posedness of incompressible two-phase flows with phase transitions: Non-equal densities with large initial data. Adv. Differential Equations 22 (2017), no. 9/10, 737--764. https://projecteuclid.org/euclid.ade/1495850458