(untitled) (Journal of Nonlinear Modeling and Analysis, 2024)
This paper devotes to consider the local existence of the strong solutions to the generalized MHD system with fractional dissipative terms Λ^2αu for the velocity field and Λ^2αb for the magnetic field, respectively. We construct the approximate solutions by the Fourier truncation method, and use energy method to obtain the local existence of strong solutions in H^s (R^n) (s > max {n2 + 1 − 2α, 0}) for any α ≥ 0.