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 Rn, n = 2, 3, for divergence-free initial data in certain Besov spaces, namely u0 ? Bn/2-1 2,1 and B0 ? Bn/2 2,1. The a priori estimates include the term t 0 u(s) 2 Hn/2 ds on the right-hand side, which thus requires an auxiliary bound in Hn/2-1. In 2D, this is simply achieved using the standard energy inequality; but in 3D an auxiliary estimate in H1/2 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 case.