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### Existence of Leray's self-similar solutions of the Navier-Stokes equations in D subset of R-3

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UNSPECIFIED.
(2004)
*Existence of Leray's self-similar solutions of the Navier-Stokes equations in D subset of R-3.*
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 47
(1).
pp. 30-37.
ISSN 0008-4395

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## Abstract

Leray's self-similar solution of the Navier-Stokes equations is defined by u(x, t) = U(y)/2root(t* - t), where y = x/root2sigma(t* - t), sigma > 0. Consider the equation for U(y) in a smooth bounded domain D of R-3 with non-zero boundary condition: -vDeltaU+sigmaU+sigmay(.)delU+U(.)delU+delP=0, y is an element of D, del(.)U=0, y is an element of D, U = 9(y), y E partial derivativeD. We prove an existence theorem for the Dirichlet problem in Sobolev space W-1,W-2(D). This implies the local existence of a self-similar solution of the Navier-Stokes equations which blows up at t = t* with t(*) < +infinity, provided the function G(y) is permissible.

Item Type: | Journal Article |
---|---|

Subjects: | Q Science > QA Mathematics |

Journal or Publication Title: | CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES |

Publisher: | CANADIAN MATHEMATICAL SOC |

ISSN: | 0008-4395 |

Date: | March 2004 |

Volume: | 47 |

Number: | 1 |

Number of Pages: | 8 |

Page Range: | pp. 30-37 |

Publication Status: | Published |

URI: | http://wrap.warwick.ac.uk/id/eprint/8773 |

Data sourced from Thomson Reuters' Web of Knowledge

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