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arXiv · 1607.04397

Global well-posedness of the MHD equations in a homogeneous magnetic field

Dongyi Wei·Zhifei Zhang
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Abstract

In this paper, we study the MHD equations with small viscosity and resistivity coefficients, which may be different. This is a typical setting in high temperature plasmas. It was proved that the MHD equations are globally well-posed if the initial velocity is close to 0 and the initial magnetic field is close to a homogeneous magnetic field in the weighted Hölder space, where the closeness is independent of the dissipation coefficients.

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Dongyi Wei, Zhifei Zhang. 2016-07-15. Global well-posedness of the MHD equations in a homogeneous magnetic field. https://doi.org/10.2140/apde.2017.10.1361

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