## Abstract

We prove a generalized resolvent estimate of Stokes equations with nonhomogeneous Robin boundary condition and divergence condition in the L _{q} framework (1 < q < ∞) in a domain of R^{n} (n ≧ 2) that is a bounded domain or the exterior of a bounded domain. The Robin condition consists of two conditions: v · u = 0 and au + β(T(u, p)v -(T(u, p)u, v)v) = h on the boundary of the domain with α, β ≧ 0 and α + β= 1, where u denotes a velocity vector, p a pressure, T(u, p) the stress tensor for the Stokes flow, and v the unit outer normal to the boundary of the domain. It presents the slip condition when β=1 and the non-slip one when α = 1, respectively.

Original language | English |
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Pages (from-to) | 469-519 |

Number of pages | 51 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 59 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2007 Apr |

## Keywords

- Resolvent estimate
- Robin boundary condition
- Stokes system

## ASJC Scopus subject areas

- Mathematics(all)