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Let $(u,b)$ be a smooth enough solution of 3-D incompressible MHD system. Weprove that if $(u,b)$ blows up at a finite time $T^*$, then for any$p\in]4,\infty[$, there holds $\int_0^{T^*}\bigl(\|u^3(t')\|^p_{\dH^{\frac12+\frac 2p}}+\|b(t')\|^p_{\dH^{\frac 12+\frac 2p}}\bigr)dt'=\infty$. We remarkthat all these quantities are in the critical regularity of the MHD system.

On the critical one-component velocity regularity criteria to 3-D incompressible MHD system