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, namely $$\sup_{j\in\mathbb{Z}}\int_0^T\|\Delta_j(\nabla\times u)\|_\infty dt,$$where Δ j is the frequency localization operator in the Littlewood-Paley decomposition.
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