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

2018/08/22 by Keiichi Watanabe, Watanabe, Keiichi
Mathematics · #35Q30 #76T10 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1808.07245

openalex publication_date 2018/08/22 · openalex created_date 2018/08/31 · openalex updated_date 2026/07/28

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

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