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Journal of Mathematical Fluid Mechanics

, Volume 9, Issue 2, pp 181–210 | Cite as

Weighted Sobolev Spaces for a Scalar Model of the Stationary Oseen Equations in \(\mathbb{R}^{3}\)

  • Chérif Amrouche
  • Ulrich Razafison
Article

Abstract.

This paper is devoted to a scalar model of the Oseen equations, a linearized form of the Navier–Stokes equations. To control the behavior of functions at infinity, the problem is set in weighted Sobolev spaces including anisotropic weights. In a first step, some weighted Poincaré-type inequalities are obtained. In a second step, we establish existence, uniqueness and regularity results.

Mathematics Subject Classification (2000).

76D05 35Q30 26D15 46D35 

Keywords.

Oseen equations anisotropic weights Poincaré inequalities Sobolev spaces unbounded domains 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques Appliquées, CNRS UMR 5142Université de Pau et des Pays de l’AdourPauFrance

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