Geodesic
The scalar Oseen operator $-\Delta + {\partial}/{\partial x_1}$ in $\mathbb{R}^2$
Applications of Mathematics, Tome 53 (2008) no. 1, pp. 41-80

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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.
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

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