On local \(L_p\)-\(L_q\) well-posedness of incompressible two-phase flows with phase transitions: non-equal densities with large initial data. (English) Zbl 06780898

Shimizu, Senjo; Yagi, Shintaro

Adv. Differ. Equ. 22, No. 9-10, 737-764 (2017).

Summary: 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.

MSC:

35R35	Free boundary problems for PDEs
35Q30	Navier-Stokes equations
76D45	Capillarity (surface tension) for incompressible viscous fluids
76T10	Liquid-gas two-phase flows, bubbly flows