Local Existence of Strong Solutions to the Generalized MHD Equations (Journal of Nonlinear Modeling and Analysis, 2024)
This paper devotes to consider the local existence of the strongsolutions to the generalized MHD system with fractional dissipative terms $Λ^{2α}u$ for the velocity field and $Λ^{2α}b$ for the magnetic field, respectively. Weconstruct the approximate solutions by the Fourier truncation method, and useenergy method to obtain the local existence of strong solutions in $H^s(\mathbb{R}^n)$ $(s >max \{\frac{n}{2} + 1 − 2α, 0\})$ for any $α ≥ 0.$
Keywords: Generalized MHD system; local existence; Fourier truncation.