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arXiv · 1610.00973

A global existence result for the anisotropic magnetohydrodynamical systems

Van-Sang Ngo
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Abstract

We study an anisotropic system arising in magnetohydrodynamics (MHD) in the whole space R^3 , in the case where there are no diffusivity in the vertical direction and only a small diffusivity in the horizontal direction (of size $\epsilon$$\alpha$ with 0 \textless{} $\alpha$ $\le$ $\alpha$0, for some $\alpha$0 \textgreater{} 0). We prove the local existence and uniqueness of a strong solution and then, using Strichartz-type estimates, we prove that this solution globally exists in time for large initial data, when the rotation is fast enough.

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Van-Sang Ngo. 2016-10-04. A global existence result for the anisotropic magnetohydrodynamical systems. https://arxiv.org/abs/1610.00973

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