In this paper, we consider the Littlewood-Paley $ p $th-order ($ 1\le p<\infty $) moments of the three-dimensional MHD periodic equations, which are defined by the infinite-time and space average of $ L^p $-norm of velocity and magnetic fields involved in the spectral cut-off operator $ \dot\Delta_m $. Our results imply that in some cases, $ k^{-\frac{1}{3}} $ is an upper bound at length scale $ 1/k $. This coincides with the scaling law of many observations on astrophysical systems and simulations in terms of 3D MHD turbulence.
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