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arXiv · 2012.02382

On 3D Hall-MHD equations with fractional Laplacians: global well-posedness

Huali Zhang·Kun Zhao
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Abstract

Cauchy problem for 3D incompressible Hall-magnetohydrodynamics (Hall-MHD) system with fractional Laplacians is studied. First, global well-posedness of small-energy solutions with general initial data in $H^s$, $s>\frac{5}{2}$, is proved. Second, a special class of large-energy initial data is constructed, with which the Cauchy problem is globally well-posed. The proofs rely upon a new global bound of energy estimates involving Littlewood-Paley decomposition and Sobolev inequalities, which enables one to overcome the $\frac{1}{2}$-order derivative loss of the magnetic field.

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Huali Zhang, Kun Zhao. 2020-12-04. On 3D Hall-MHD equations with fractional Laplacians: global well-posedness. https://doi.org/10.1007/s00021-021-00605-y

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