### 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 |
---|---|

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 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**On the maximal L _{p}-L _{q} regularity of the Stokes problem with first order boundary condition; model problems.** / Shibata, Yoshihiro; Shimizu, Senjo.

Research output: Contribution to journal › Article

_{p}-L

_{q}regularity of the Stokes problem with first order boundary condition; model problems',

*Journal of the Mathematical Society of Japan*, vol. 64, no. 2, pp. 561-626. https://doi.org/10.2969/jmsj/06420561

}

TY - JOUR

T1 - On the maximal L p-L q regularity of the Stokes problem with first order boundary condition; model problems

AU - Shibata, Yoshihiro

AU - Shimizu, Senjo

PY - 2012

Y1 - 2012

N2 - 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}

AB - 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}

KW - Gravity force

KW - Half space problem

KW - Maximal regularity

KW - Resolvent estimate

KW - Stokes equation

KW - Surface tension

UR - http://www.scopus.com/inward/record.url?scp=84867037698&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867037698&partnerID=8YFLogxK

U2 - 10.2969/jmsj/06420561

DO - 10.2969/jmsj/06420561

M3 - Article

VL - 64

SP - 561

EP - 626

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 2

ER -