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September  2003, 2(3): 381-390. doi: 10.3934/cpaa.2003.2.381

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

Hideo Ikeda 1, , Koji Kondo 2, , Hisashi Okamoto 3, and  Shoji Yotsutani 4,

1. 

Department of Mathematics, Toyama University, Gofuku, Toyama, 930-8555, Japan
2. 

TIS System Service Inc., Koto, Tokyo, 135-0016, Japan
3. 

Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan
4. 

Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu 520-2194, Japan

Received  January 2003 Revised  April 2003 Published  June 2003

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, 76D0.
Citation: Hideo Ikeda, Koji Kondo, Hisashi Okamoto, Shoji Yotsutani. On the global branches of the solutions to a nonlocal boundary-value problem arising in Oseen's spiral flows. Communications on Pure & Applied Analysis, 2003, 2 (3) : 381-390. doi: 10.3934/cpaa.2003.2.381
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