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

Fefferman, Charles L, McCormick, David S, Robinson, James C and Rodrigo, Jose L (2015) Higher order commutator estimates and local existence for the non-resistive MHD equations and related models. Journal of Functional Analysis, 267 (4). pp. 1035-1056. ISSN 0022-1236

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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 & Ponce (Comm. Pure Appl. Math. 41(7), 891–907, 1988).

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Numerical Analysis and Scientific Computing Research Group
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
Depositing User: David McCormick
Date Deposited: 12 Jan 2017 11:27
Last Modified: 08 Mar 2017 06:05
URI: http://sro.sussex.ac.uk/id/eprint/59610

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