On a Stationary Problem of the Stokes Equation in an Infinite Layer in Sobolev and Besov Spaces |
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| Authors: | Takayuki Abe Masao Yamazaki |
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| Affiliation: | 1. Kisarazu National College of Technology, Kiyomidai-Higashi 2-11-1, Kisarazu, Chiba, 292-0041, Japan
2. Department of Mathematical Sciences, School of Science and Engineering, Waseda University, Ohkubo 3-4-1, Shinjuku-ku, Tokyo, 169-8555, Japan
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| Abstract: | This paper is concerned with the stationary problem of the Stokes equation in an infinite layer and provides a condition on the external force sufficient for the existence of the solution. Since the Poiseuille flow is a solution to the homogeneous equation, the solution is not unique when p = ∞. It is also proved that, under some suitable conditions, solutions to the homogeneous equation are limited only to the Poiseuille flow. |
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