### Abstract

In this paper, we proved the generalized resolvent estimate and the maximal L _{p}-L _{q} regularity of the Stokes equation with first order boundary condition in the half-space, which arises in the mathematical study of the motion of a viscous incompressible one phase fluid flow with free surface. The core of our approach is to prove the R boundedness of solution operators defined in a sector Σ _{∈,γ0} = {λ ∈ C \ {0}

Original language | English |
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Pages (from-to) | 561-626 |

Number of pages | 66 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 64 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2012 Oct 9 |

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### Keywords

- Gravity force
- Half space problem
- Maximal regularity
- Resolvent estimate
- Stokes equation
- Surface tension

### ASJC Scopus subject areas

- Mathematics(all)