On the local well-posedness of strong solutions to 3D MHD equations with Hall and ion-slip effects

In this paper, through maximal regularity estimates for the Stokes equation, we study the local well-posedness of strong solutions to the 3D MHD equations with Hall and ion-slip effects under the condition that the initial data $(u_0,B_0)\in H^{\frac{1}{2}+\epsilon }\left(R^3\right)\times H^2\left(R^3\right)$ and any $\epsilon \in (0,1)$. This is an improvement of the recent results given by Fan et al. (Z Angew Math Phys, 2015).