2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171050We 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 $|ξ|\approx 2^j$.12pagesAnalysis of PDEs76W05, 35B65text