On the ℛ-boundedness for the two phase problem: compressible-incompressible model problem

Takayuki Kubo, Yoshihiro Shibata, Kohei Soga

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The situation of this paper is that the Stokes equation for the compressible viscous fluid flow in the upper half-space is coupled via inhomogeneous interface conditions with the Stokes equations for the incompressible one in the lower half-space, which is the model problem for the evolution of compressible and incompressible viscous fluid flows with a sharp interface. We show the existence of ℛ-bounded solution operators to the corresponding generalized resolvent problem, which implies the generation of analytic semigroup and maximal Lp-Lq regularity for the corresponding time dependent problem with the help of the Weis’ operator valued Fourier multiplier theorem. The problem was studied by Denisova (Interfaces Free Bound. 2(3):283-312, 2000) under some restriction on the viscosity coefficients and one of our purposes is to eliminate the assumption in (Denisova in Interfaces Free Bound. 2(3):283-312, 2000).

Original languageEnglish
Article number141
Pages (from-to)1-33
Number of pages33
JournalTijdschrift voor Urologie
Volume2014
Issue number1
DOIs
Publication statusPublished - 2014 Jan 17

Keywords

  • Stokes equations
  • compressible-incompressible two phase problem
  • generalized resolvent problem
  • model problem
  • ℛ-boundedness

ASJC Scopus subject areas

  • Urology

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