Formula omitted]-inequalities for scalar Oseen potential

Abstract

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 − Δ + ∂ ∂ x 1 . The Marcinkiewicz interpolation's theorem and the Sobolev embeddings are used to give, in the L p theory, the continuity's properties of the scalar Oseen potential. The contribution of the term ∂ ∂ x 1 gives supplementary properties with regard to the Riesz potential.