Global Solvability of Compressible–Incompressible Two-Phase Flows with Phase Transitions in Bounded Domains

Consider a free boundary problem of compressible-incompressible two-phase flows with surface tension and phase transition in bounded domains Ωt+,Ωt−⊂RN, N≥2, where the are separated by sharp compact interface Γt⊂RN−1. We prove global time unique existence theorem for such under assumption that initial data sufficiently small domain incompressible fluid is close to ball. In particular, we obtain solution maximal Lp−Lq-regularity class 2<p<∞ N<q<∞ exponential stability corresponding analytic semigroup on infinite interval.