Lp-inequalities for scalar Oseen potential

The Oseen equations are obtained by linearizing the Navier–Stokes equations around a nonzero constant vector which is the velocity at infinity.We are interested with the study of the scalar problem corresponding to the anisotropic operator − + ∂ ∂x1 . The Marcinkiewicz interpolation’s theorem and the Sobolev embeddings are used to give, in the Lp theory, the continuity’s properties of the scalar Oseen potential. The contribution of the term ∂ ∂x1 gives supplementary properties with regard to the Riesz potential. © 2007 Elsevier Inc. All rights reserved.