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

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 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**L _{p}-L _{q} maximal regularity and viscous incompressible flows with free surface.** / Shibata, Yoshihiro; Shimizu, Senjo.

Research output: Contribution to journal › Article

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_{q}maximal regularity and viscous incompressible flows with free surface',

*Proceedings of the Japan Academy Series A: Mathematical Sciences*, vol. 81, no. 9, pp. 151-155. https://doi.org/10.3792/pjaa.81.151

}

TY - JOUR

T1 - L p-L q maximal regularity and viscous incompressible flows with free surface

AU - Shibata, Yoshihiro

AU - Shimizu, Senjo

PY - 2005/11

Y1 - 2005/11

N2 - 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.

AB - 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.

KW - Free boundary problem

KW - Maximal regularity

KW - Navier-Stokes equations

KW - Neumann boundary condition

KW - Stokes equations

UR - http://www.scopus.com/inward/record.url?scp=30444459643&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=30444459643&partnerID=8YFLogxK

U2 - 10.3792/pjaa.81.151

DO - 10.3792/pjaa.81.151

M3 - Article

AN - SCOPUS:30444459643

VL - 81

SP - 151

EP - 155

JO - Proceedings of the Japan Academy Series A: Mathematical Sciences

JF - Proceedings of the Japan Academy Series A: Mathematical Sciences

SN - 0386-2194

IS - 9

ER -