Resumen de Study of the scalar oseen equation

U. Razafison, Chérif Amrouche

• This paper is devoted to the scalar Oseen equation, a linearized form of the Navier- Stokes equations. Because of the various decay properties in various directions of RN, the problem is set in Sobolev spaces with anisotropic weights. In a first step, some weighted Hardy-type inequalities are obtained, which yield some norm equivalences. In a second step, we establish existence results.