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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
Full text not available from this repository.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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