We obtain lower bounds on blow-up of solutions for the 3D magneto-micropolar equations. More precisely, we establish some estimates for the solution (u,w,b)(t)\documentclass[12pt]{minimal}
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\begin{document}$(\mathbf{u},\mathbf{w},\mathbf{b}) (t)$\end{document} in its maximal interval [0,T∗)\documentclass[12pt]{minimal}
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\begin{document}$[0,T^{*})$\end{document} provided that T∗<∞\documentclass[12pt]{minimal}
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\begin{document}$T^{*}<\infty$\end{document}, which show for δ∈(0,1)\documentclass[12pt]{minimal}
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\begin{document}$\delta\in(0,1)$\end{document} that ∥(u,w,b)(t)∥H˙s\documentclass[12pt]{minimal}
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\begin{document}$\|(\mathbf{u},\mathbf{w},\mathbf{b})(t)\|_{\dot{H}^{s}}$\end{document} is at least of the order (T∗−t)−(δs)/(1+2δ)\documentclass[12pt]{minimal}
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\begin{document}$(T^{*}-t)^{-(\delta s)/(1+2\delta)}$\end{document} for s≥1/2+δ\documentclass[12pt]{minimal}
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\begin{document}$s\geq1/2+\delta$\end{document}. In particular, by choosing a suitable δ\documentclass[12pt]{minimal}
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\begin{document}$\delta$\end{document}, one concludes that ∥(u,w,b)(t)∥H˙s\documentclass[12pt]{minimal}
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\begin{document}$\|(\mathbf{u},\mathbf{w},\mathbf{b})(t)\|_{\dot{H}^{s}}$\end{document} is at least of the order (T∗−t)−s/4\documentclass[12pt]{minimal}
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\begin{document}$(T^{*}-t)^{-s/4}$\end{document}, and (T∗−t)1/4−s/2\documentclass[12pt]{minimal}
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\begin{document}$(T^{*}-t)^{1/4-s/2}$\end{document} for s≥1\documentclass[12pt]{minimal}
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\begin{document}$s\geq1$\end{document}, and 1/2<s<3/2\documentclass[12pt]{minimal}
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\begin{document}$1/2< s<3/2$\end{document}, respectively. We also show that (T∗−t)−s/3\documentclass[12pt]{minimal}
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\begin{document}$(T^{*}-t)^{-s/3}$\end{document} is a lower rate for ∥(u,w,b)(t)∥H˙s\documentclass[12pt]{minimal}
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\begin{document}$\|(\mathbf{u},\mathbf{w},\mathbf{b})(t)\|_{\dot{H}^{s}}$\end{document} if s>3/2\documentclass[12pt]{minimal}
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\begin{document}$s>3/2$\end{document}.
