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Journal of Mathematical Fluid Mechanics

, Volume 12, Issue 1, pp 61–100 | Cite as

On a Stationary Problem of the Stokes Equation in an Infinite Layer in Sobolev and Besov Spaces

  • Takayuki AbeEmail author
  • Masao Yamazaki
Article

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.

Keywords.

Stokes equation stationary problem infinite layer Sobolev space Besov space homogeneous Besov space Poiseuille flow 

Mathematics Subject Classification (2000).

Primary 35Q30 secondary 76D07 

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Copyright information

© Birkhäuser Verlag, Basel 2008

Authors and Affiliations

  1. 1.Kisarazu National College of TechnologyChibaJapan
  2. 2.Department of Mathematical Sciences, School of Science and EngineeringWaseda UniversityTokyoJapan

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