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 language | English |
|---|---|
| Pages (from-to) | 1-33 |
| Number of pages | 33 |
| Journal | Tijdschrift voor Urologie |
| Volume | 2014 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2014 Jan 17 |
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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 journal › Article
}
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
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 - compressible-incompressible two phase problem
KW - generalized resolvent problem
KW - model problem
KW - Stokes equations
KW - ℛ-boundedness
UR - http://www.scopus.com/inward/record.url?scp=84919399315&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84919399315&partnerID=8YFLogxK
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
ER -