### 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 L_{p}-L_{q} 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 |
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Article number | 141 |

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

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

### ASJC Scopus subject areas

- Urology

### Cite this

*Tijdschrift voor Urologie*,

*2014*(1), 1-33. [141]. https://doi.org/10.1186/s13661-014-0141-3