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Pré-Publication, Document De Travail Année : 2007

$L^p$-Inequalities for Scalar Oseen Potential

Résumé

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$−\Delta + \frac{\partial}{\partial x_1}$. 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 $\frac{\partial}{\partial x_1}$ gives supplementary properties with regard to the Riesz potential.
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Dates et versions

hal-00199727 , version 1 (19-12-2007)

Identifiants

  • HAL Id : hal-00199727 , version 1

Citer

Chérif Amrouche, Hamid Bouzit. $L^p$-Inequalities for Scalar Oseen Potential. 2007. ⟨hal-00199727⟩
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