$L^p$-Inequalities for Scalar Oseen Potential

Chérif Amrouche (1) , Hamid Bouzit (1, 2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Département de Mathématiques, Université de Mostaganem

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.

Mots clés: $L^p$-theory; Oseen potential; weighted Sobolev spaces; $L^p$-theory.

Domaines: Equations aux dérivées partielles [math.AP]

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