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This paper establishes the local-in-time existence and uniqueness of strongsolutions in $H^{s}$ for $s > n/2$ to the viscous, non-resistivemagnetohydrodynamics (MHD) equations in $\mathbb{R}^{n}$, $n=2, 3$, as well asfor a related model where the advection terms are removed from the velocityequation. The uniform bounds required for proving existence are established bymeans of a new estimate, which is a partial generalisation of the commutatorestimate of Kato & Ponce (Comm. Pure Appl. Math. 41(7), 891-907, 1988).

Higher order commutator estimates and local existence for the non-resistive MHD equations and related models