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Well-posedness and finite element approximation of the electrostatic shear Alfv\'en wave equations
new Abstract: The aim of this paper is to study the well-posedness and finite element approximation of the electrostatic shear Alfv\'en wave equations, a coupled system of two partial differential equations arising in plasma physics as a simplified sub-model of the drift-reduced Braginskii equations. To this end, anisotropic Sobolev spaces depending on the normalized magnetic field $\b$ are introduced, together with a Poincar\'e-type inequality along the integral curves of $\b$, which holds...