Global solvability of compressible–incompressible two-phase flows with phase transitions in bounded domains

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Abstract

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 domains are separated by a sharp compact interface Γt ⊂ RN−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 Lp − Lq-regularity class with 2 < p < ∞ and N < q < ∞ and exponential stability of the corresponding analytic semigroup on the infinite time interval.

Original languageEnglish
Article number258
Pages (from-to)1-28
Number of pages28
JournalMathematics
Volume9
Issue number3
DOIs
Publication statusPublished - 2021

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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