TY - JOUR

T1 - On the ℛ-boundedness for the two phase problem

T2 - compressible-incompressible model problem

AU - Kubo, Takayuki

AU - Shibata, Yoshihiro

AU - Soga, Kohei

N1 - Publisher Copyright:
© 2014, Kubo et al.; licensee Springer.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

PY - 2014/1/17

Y1 - 2014/1/17

N2 - 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).

AB - 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).

KW - Stokes equations

KW - compressible-incompressible two phase problem

KW - generalized resolvent problem

KW - model problem

KW - ℛ-boundedness

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U2 - 10.1186/s13661-014-0141-3

DO - 10.1186/s13661-014-0141-3

M3 - Article

AN - SCOPUS:84919399315

VL - 2014

SP - 1

EP - 33

JO - Tijdschrift voor Urologie

JF - Tijdschrift voor Urologie

SN - 2211-3037

IS - 1

M1 - 141

ER -