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

@inproceedings{Fefferman2017HigherOC,
title={Higher order commutator estimates and local existence for the non-resistive MHD equations and related models},
author={Charles Fefferman and David S. McCormick and James C. Robinson and Jos{\'e} L. Rodrigo},
year={2017}
}

This paper establishes the local-in-time existence and uniqueness of strong solutions in H for s > n/2 to the viscous, non-resistive magnetohydrodynamics (MHD) equations in R, 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… CONTINUE READING