Compressible-incompressible two-phase flows with phase transition: Model problem

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We study the compressible and incompressible two-phase flows separated by a sharp interface with a phase transition and a surface tension. In particular, we consider the problem in RN, and the Navier-Stokes-Korteweg equations is used in the upper domain and the Navier-Stokes equations is used in the lower domain. We prove the existence of R-bounded solution operator families for a resolvent problem arising from its model problem. According to Shibata [13], the regularity of ρ+ is Wq1 in space, but to solve the kinetic equation: uΓ · nt = [[ρu]] · nt/[[ρ]] on Γt we need Wq2−1/q regularity of ρ+ on Γt, which means the regularity loss. Since the regularity of ρ+ dominated by the Navier-Stokes-Korteweg equations is Wq3 in space, we eliminate the problem by using the Navier-Stokes-Korteweg equations instead of the compressible Navier-Stokes equations.

MSC Codes 35Q30 (Primary), 76T10 (Secondary)

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2017 May 9


  • Compressible and incompressible viscous flow
  • Maximal Lp-Lq regularity
  • Navier-Stokes-Korteweg equation
  • Phase transition
  • R-bounded solution operator
  • Surface tension
  • Two-phase flows

ASJC Scopus subject areas

  • General

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