Throughout this note m≥3 and either Ω=Rm, or Ω is a half-space of Rm, or Ω is a smooth domain in Rm with a compact boundary ∂Ω. We consider the following initial-boundary value problem (1) for the Navier-Stokes equations:

∇⋅v∂tv+(v⋅∇)v−νΔvvv(⋅,0)=0=−∇p=0=v0in Ω,in Ω,on ∂Ω,in Ω.

Of course, there is no boundary condition if Ω=Rm.

"In a recent paper [J. Math. Fluid Mech. 2 (2000), no. 1, 16--98] we investigated the strong solvability of (1) for initial data v0 belonging to certain spaces of distributions (modulo gradients). In this note we explain some of our main results in a very particular and simple setting. As usual, we concentrate on the velocity field v since the pressure field p is determined up to a constant by v.

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Amann, H (2001). *Remarks on the strong solvability of the Navier-Stokes equations.* Functional Differential Equations, 8(1-2):3-9.

## Abstract

Throughout this note m≥3 and either Ω=Rm, or Ω is a half-space of Rm, or Ω is a smooth domain in Rm with a compact boundary ∂Ω. We consider the following initial-boundary value problem (1) for the Navier-Stokes equations:

∇⋅v∂tv+(v⋅∇)v−νΔvvv(⋅,0)=0=−∇p=0=v0in Ω,in Ω,on ∂Ω,in Ω.

Of course, there is no boundary condition if Ω=Rm.

"In a recent paper [J. Math. Fluid Mech. 2 (2000), no. 1, 16--98] we investigated the strong solvability of (1) for initial data v0 belonging to certain spaces of distributions (modulo gradients). In this note we explain some of our main results in a very particular and simple setting. As usual, we concentrate on the velocity field v since the pressure field p is determined up to a constant by v.

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## Additional indexing

Other titles: | International Conference on Differential and Functional Differential Equations (Moscow, 1999) |
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Item Type: | Journal Article, refereed, original work |

Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Uncontrolled Keywords: | maximal strong solution; Leray-Hopf weak solutions; exterior forces |

Language: | English |

Date: | 2001 |

Deposited On: | 29 Nov 2010 16:27 |

Last Modified: | 05 Apr 2016 13:25 |

Publisher: | Ariel University Center of Samaria |

ISSN: | 0793-1786 |

Additional Information: | © 2001 Ariel University Center of Samaria - All Rights Reserved. |

Official URL: | http://www.hit.ac.il/staff/benzionS/FDE.html |

Related URLs: | http://www.ams.org/mathscinet-getitem?mr=1949984 http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1060.35102 |

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