Isotropically and Anisotropically Weighted Sobolev Spaces for the Oseen Equation

Chérif Amrouche (1) , Ulrich Razafison (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

This contribution is devoted to the Oseen equations, a linearized form of the Navier-Stokes equations. We give here some results concerning the scalar Oseen operator and we prove Hardy inequalities concerning functions in Sobolev spaces with anisotropic weights that appear in the investigation of the Oseen equations.

Mots clés: Oseen equations; anisotropic weights; Hardy inequality; Sobolev weighted spaces

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, Ulrich Razafison. Isotropically and Anisotropically Weighted Sobolev Spaces for the Oseen Equation. Advances in Mathematical Fluid Mechanics, 2010, pp.1-24. ⟨10.1007/978-3-642-04068-9_1⟩. ⟨hal-00335163⟩