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arXiv · 2310.09732

On the energy method for the global solutions to the three dimensional incompressible non-resistive MHD near equilibrium

Yuan Cai·Bin Han·Na Zhao
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Abstract

We prove the global existence of the smooth solutions near equilibrium to the Cauchy problem of the incompressible non-resistive magnetohydrodynamic equations in the whole three dimensional space under some admissible condition. The result has been obtained by Xu and Zhang (SIAM J. Math. Anal. 47: 26--65, 2015) in anisotropic Besov space framework. In this paper, we provide a new proof based on the temporal weighted energy method.

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Yuan Cai, Bin Han, Na Zhao. 2023-10-15. On the energy method for the global solutions to the three dimensional incompressible non-resistive MHD near equilibrium. https://arxiv.org/abs/2310.09732

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