Journal of Mathematical Fluid Mechanics

, Volume 2, Issue 4, pp 353–364 | Cite as

On the Asymptotic Behavior of Physically Reasonable Solutions to the Stationary Navier—Stokes System in Three-dimensional Exterior Domains with Zero Velocity at Infinity

  • P. Deuring
  • G. P. Galdi

Abstract.

We consider physically reasonable solutions of the stationary Navier—Stokes system in a three-dimensional exterior domains with zero velocity at infinity. We show that when these solutions are asymptotically expanded near infinity, the leading term cannot be the product of a non-zero vector with the Stokes fundamental solution. This result should be contrasted with the case when the velocity at infinity is not zero. Then, as is well known, such an expansion is possible, with the leading term being the product of a suitable constant vector with the fundamental Oseen solution.

Keywords. Navier—Stokes system, 3D exterior domains, physically reasonable solutions, asymptotic behavior. 

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Copyright information

© Birkhäuser Verlag, Basel, 2000

Authors and Affiliations

  • P. Deuring
    • 1
  • G. P. Galdi
    • 2
  1. 1.Université du Littoral, Centre Universitaire de la Mi-Voix, Laboratoire de Mathématiques Pures et Appliquées, B.P. 699, F-62228 Calais, France FR
  2. 2.Department of Mechanical Engineering, 630 Benedum Hall, University of Pittsburgh, Pittsburgh, PA 15261, USA US

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