The scalar Oseen operator $−\Delta + \frac{\partial}{\partial x_1}$ in $\mathbb{R^2}$.

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

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

This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has an anisotropic properties, the problem is set in Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in $L^p$ theory.

Mots clés: Oseen equations; weighted Sobolev spaces; anisotropic weights.; anisotropic weights

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, Hamid Bouzit. The scalar Oseen operator $−\Delta + \frac{\partial}{\partial x_1}$ in $\mathbb{R^2}$.. 2007. ⟨hal-00199722⟩