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arXiv · 2011.04043

Hydrostatic approximation of the 2D MHD system in a thin strip with a small analytic data

Nacer Aarach
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Abstract

In this paper, we study the global well-posedness of the two dimensional rescaled anisotropic MHD system and also to the hydrostatic MHD with no slip boundary condition in a strip, for small initial data, which are analytic in the horizontal variable. We also justify the limit of the MHD system (when $\epsilon\to 0$ where $\epsilon$ denotes the height of the initial strip) is given by a couple of a Prandtl like system for the velocity and a magnetic field equation when the initial data are small and analytic.

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Nacer Aarach. 2020-11-08. Hydrostatic approximation of the 2D MHD system in a thin strip with a small analytic data. https://doi.org/10.1016/j.jmaa.2021.125949

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