Local existence for the non-resistive magnetohydrodynamic system with fractional dissipation in the Lp framework

In this paper, we consider the Cauchy problem of the d-dimensional magnetohydrodynamic (MHD) system with the fractional dissipation (-Delta)(alpha)u and without the magnetic diffusion. We obtain the local existence and uniqueness of the solution to the non-resistive MHD system in the L-P framework under two cases: alpha >= 1 and alpha < 1. Our result improves considerably the recent results in Chemin et al. (Adv Math 286:1-31, 2016), Jiu et al. (Commun Math Sci 18:987-1022, 2020), Li et al. (Adv Math 317:786-798, 2017), and Wan (Nonlinear Anal Real World Appl 30:32-40, 2016), which can be regarded as a generalization of these works.