Strong solutions to compressible-incompressible two-phase flows with phase transitions

We consider a free boundary problem of compressible-incompressible two-phase flows with phase transitions in general domains of N-dimensional Euclidean space (e.g. whole space; half-spaces; bounded domains; exterior domains). The compressible fluid and the incompressible fluid are separated by either compact or non-compact sharp moving interface, and the surface tension is taken into account. In our model, the compressible fluid and incompressible fluid are occupied by the Navier-Stokes-Korteweg equations and the Navier-Stokes equations, respectively. This paper shows that for given T > 0 the problem admits a unique strong solution on (0, T) in the maximal L-p - L-q regularity class provided the initial data are small in their natural norms. (C) 2020 Elsevier Ltd. All rights reserved.