## Abstract

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.

Original language | English |
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Article number | 103101 |

Journal | Nonlinear Analysis: Real World Applications |

Volume | 54 |

DOIs | |

Publication status | Published - 2020 Aug |

## Keywords

- Free boundary problem
- Maximal regularity
- Phase transition
- Two-phase problem

## ASJC Scopus subject areas

- Analysis
- Engineering(all)
- Economics, Econometrics and Finance(all)
- Computational Mathematics
- Applied Mathematics