### Abstract

We prove the L _{p}-L _{q} maximal regularity of solutions to the Neumann problem for the Stokes equations with non-homogeneous boundary condition and divergence condition in a bounded domain. And as an application, we consider a free boundary problem for the Navier-Stokes equation. We prove a locally in time unique existence of solutions to this problem for any initial data and a globally in time unique existence of solutions to this problem for some small initial data.

Original language | English |
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Pages (from-to) | 151-155 |

Number of pages | 5 |

Journal | Proceedings of the Japan Academy Series A: Mathematical Sciences |

Volume | 81 |

Issue number | 9 |

DOIs | |

Publication status | Published - 2005 Nov 1 |

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### Keywords

- Free boundary problem
- Maximal regularity
- Navier-Stokes equations
- Neumann boundary condition
- Stokes equations

### ASJC Scopus subject areas

- Mathematics(all)