The scalar Oseen operator $-\Delta + {\partial}/{\partial x_1}$ in $\mathbb{R}^2$

Amrouche, Chérif; Bouzit, Hamid

doi:10.1007/s10492-008-0012-2

Geodesic

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The scalar Oseen operator $-\Delta + {\partial}/{\partial x_1}$ in $\mathbb{R}^2$

Amrouche, Chérif ; Bouzit, Hamid

Applications of Mathematics, Tome 53 (2008) no. 1, pp. 41-80.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Résumé

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

MR Zbl

DOI : 10.1007/s10492-008-0012-2

Classification : 26D15, 35Q30, 35Q35, 76D03, 76D05
Keywords: Oseen equation; weighted Sobolev space; anisotropic weight

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Amrouche, Chérif; Bouzit, Hamid. The scalar Oseen operator $-\Delta + {\partial}/{\partial x_1}$ in $\mathbb{R}^2$. Applications of Mathematics, Tome 53 (2008) no. 1, pp. 41-80. doi : 10.1007/s10492-008-0012-2. http://geodesic.mathdoc.fr/articles/10.1007/s10492-008-0012-2/

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