Global Solvability of Compressible–Incompressible Two-Phase Flows with Phase Transitions in Bounded Domains

Keiichi Watanabe
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Keiichi Watanabe: Global Center for Science and Engineering, Waseda University, 3-4-1 Ookubo, Shinjuku-ku, Tokyo 169-8555, Japan

Mathematics, 2021, vol. 9, issue 3, 1-28

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.

Keywords: free boundary problem; phase transtion; two-phase problem; global solvability; maximal regularity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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