Local existence for the non-resistive MHD equations in Besov spaces

In this paper we prove the existence of solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations on the whole of , , for divergence-free initial data in certain Besov spaces, namely and . The a priori estimates include the term on the right-hand side, which thus requires an auxiliary bound in . In 2D, this is simply achieved using the standard energy inequality; but in 3D an auxiliary estimate in is required, which we prove using the splitting method of Calderón (1990) [2]. By contrast, our proof that such solutions are unique only applies to the 3D cas