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The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations

Qionglei Chen·Changxing Miao·Zhifei Zhang
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Abstract

We study the blow-up criterion of smooth solutions to the 3D MHD equations. By means of the Littlewood-Paley decomposition, we prove a Beale-Kato-Majda type blow-up criterion of smooth solutions via the vorticity of velocity only, i. e. $\sup_{j\in\Z}\int_0^T\|Δ_j(\na\times u)\|_\infty dt$, where $Δ_j$ is a frequency localization on $|ξ|\approx 2^j$.

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Qionglei Chen, Changxing Miao, Zhifei Zhang. 2007-01-02. The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations. https://doi.org/10.1007/s00220-007-0319-y

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