On local \(L_p\)-\(L_q\) well-posedness of incompressible two-phase flows with phase transitions: the case of non equal densities. (English) Zbl 1363.35378

Shimizu, Senjo; Yagi, Shintaro

Differ. Integral Equ. 28, No. 1-2, 29-58 (2015).

Summary: 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 J. Prüss and S. Shimizu [J. Evol. Equ. 12, No. 4, 917–941 (2012; Zbl 1259.35226)]. In this paper, we prove local well-posedness of the model \(L_p\) in time \(L_q\) in space settting.

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

Keywords:

local well-posedness; phase transition

Citations:

Zbl 1259.35226