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  under a smallness assumption for the initial data. In this paper, we remove the smallness assumption for the initial data.
"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 (9/10) 737 - 764, September/October 2017. https://doi.org/10.57262/ade/1495850458