# American Institute of Mathematical Sciences

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

 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.
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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