2014 •
Higher order commutator estimates and local existence for the non-resistive MHD equations and related models
Authors: Fefferman, Charles L, McCormick, David S, Robinson, James C, Rodrigo, Jose L
Venue: Journal of Functional Analysis
Type: Publication
Abstract: This paper establishes the local-in-time existence and uniqueness of strong solutions in Hs for s > n/2 to the viscous, non-resistive magnetohydrodynamics (MHD) equations in Rn, n = 2, 3, as well as for a related model where the advection terms are removed from the velocity equation. The uniform bounds required for proving existence are established by means of a new estimate, which is a partial generalisation of the commutator estimate of Kato & Ponce (Comm. Pure Appl. Math. 41(7), 891–907, 1988).
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