  This paper establishes the local-in-time existence and uniqueness of
solutions to the viscous, non-resistive magnetohydrodynamics (MHD) equations in
$\mathbb{R}^d$, $d=2,3$, with initial data $B_0\in H^s(\mathbb{R}^d)$ and
$u_0\in H^{s-1+\varepsilon}(\mathbb{R}^d)$ for $s>d/2$ and any
$0<\varepsilon<1$. The proof relies on maximal regularity estimates for the
Stokes equation. The obstruction to taking $\varepsilon=0$ is explained by the
failure of solutions of the heat equation with initial data $u_0\in H^{s-1}$ to
satisfy $u\in L^1(0,T;H^{s+1})$; we provide an explicit example of this
phenomenon.
