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 domains are separated by a sharp compact interface Γt⊂RN−1. We prove a global in time unique existence theorem for such free boundar...

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Bibliographic Details
Published in:Mathematics (Basel) 2021, Vol.9 (3), p.258
Main Author: Watanabe, Keiichi
Format: Article
Language:English
Subjects:
Boundary conditions
Compressibility
Domains
Existence theorems
Fluid dynamics
Fluid flow
Food science
Fourier transforms
Free boundaries
free boundary problem
global solvability
Incompressible flow
Incompressible fluids
maximal regularity
Phase transitions
phase transtion
Stability analysis
Surface tension
Two phase flow
two-phase problem
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Summary: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
ISSN:2227-7390
2227-7390
DOI:10.3390/math9030258