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