Higher order commutator estimates and local existence for the non-resistive MHD equations and related models |
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Authors: | Charles L Fefferman David S McCormick James C Robinson Jose L Rodrigo |
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Institution: | 1. Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544, USA;2. Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK |
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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 and Ponce (1988) 13]. |
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Keywords: | Commutator estimates Magnetohydrodynamics MHD |
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