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

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    Viscosity

    Keywords

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

    ASJC Scopus subject areas

    • Urology

    Cite this

    On the ℛ-boundedness for the two phase problem : compressible-incompressible model problem. / Kubo, Takayuki; Shibata, Yoshihiro; Soga, Kohei.

    In: Tijdschrift voor Urologie, Vol. 2014, No. 1, 17.01.2014, p. 1-33.

    Research output: Contribution to journalArticle

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