The Littlewood-Paley Pth-Order Moments In Three-Dimensional Mhd Turbulence

In this paper, we consider the Littlewood-Paley pth-order (1 <= p < infinity) 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 (Delta) over dot(m). Our results imply that in some cases, k(-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.