## 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

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
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