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July  2021, 41(7): 3045-3062. doi: 10.3934/dcds.2020397

## The Littlewood-Paley $pth$-order moments in three-dimensional MHD turbulence

 School of Mathematics and Systems Science, Beihang University, Beijing 100191, China

* Corresponding author: Jia Yuan

Received  July 2020 Revised  October 2020 Published  July 2021 Early access  December 2020

Fund Project: The work is supported by NSF grant No.11871087 and No.11771423. The first author is supported by the Academic Excellence Foundation of BUAA for PhD students and China Scholarship Council No.201906020100

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.

Citation: Yao Nie, Jia Yuan. The Littlewood-Paley $pth$-order moments in three-dimensional MHD turbulence. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 3045-3062. doi: 10.3934/dcds.2020397
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