## Abstract

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

Original language | English |
---|---|

Article number | 258 |

Pages (from-to) | 1-28 |

Number of pages | 28 |

Journal | Mathematics |

Volume | 9 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2021 |

## Keywords

- Free boundary problem
- Global solvability
- Maximal regularity
- Phase transtion
- Two-phase problem

## ASJC Scopus subject areas

- Mathematics(all)