On the global branches of the solutions to a nonlocal boundary-value problem arising in Oseen's spiral flows

Hideo Ikeda; Koji Kondo; Hisashi Okamoto; Shoji Yotsutani

doi:10.3934/cpaa.2003.2.381

Article Contents

2003, Volume 2, Issue 3: 381-390. Doi: 10.3934/cpaa.2003.2.381

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On the global branches of the solutions to a nonlocal boundary-value problem arising in Oseen's spiral flows

1.
Department of Mathematics, Toyama University, Gofuku, Toyama, 930-8555
2.
TIS System Service Inc., Koto, Tokyo, 135-0016
3.
Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502
4.
Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu 520-2194

Received: December 31, 2002

Revised: March 31, 2003

Published: August 2003

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Abstract

We consider a parameterized, nonlocally constrained boundary-value problem, whose solutions are known to yield exact solutions, called Oseen's spiral flows, of the Navier-Stokes equations. We represent all solutions explicitly in terms of elliptic functions, and clarify completely the structure of the set of all the global branches of the solutions.

Keywords:

Nonlocal boundary value problem,
Navier-Stokes flow.

Mathematics Subject Classification: 34B15, 35C05, 76D05.

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On the global branches of the solutions to a nonlocal boundary-value problem arising in Oseen's spiral flows

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