  The spectral slope of Magnetohydrodynamic (MHD) turbulence varies depending
on the spectral theory considered; $ -3/2 $ is the spectral slope in
Kraichnan-Iroshnikov-Dobrowolny (KID) theory, $ -5/3 $ in
Marsch-Matthaeus-Zhou's and Goldreich-Sridhar theories also called
Kolmogorov-like (K-41 like) MHD theory, combination of the $-5/3$ and $-3/2$
scales in Biskamp and so on. A rigorous mathematical proof to any of these
spectral theories is of great scientific interest. Motivated by the 2012 work
of A. Biryuk and W. Craig [Physica D 241(2012) 426-438], we establish inertial
range bounds for K-41 like phenomenon in MHD turbulent flow through a
mathematical rigour; a range of wave numbers in which the spectral slope of MHD
turbulence is proportional to $-5/3$ is established and the upper and lower
bounds of this range are explicitly formulated. We also have shown that the
Leray weak solution of the standard MHD model is bonded in the Fourier space,
the spectral energy of the system is bounded and its average over time
decreases in time.

Analysis of PDEs