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

Charles L. Fefferman; David S. McCormick; James C. Robinson; Jose L. Rodrigo

doi:10.1016/j.jfa.2014.03.021

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

Charles L. Fefferman
, David S. McCormick
, James C. Robinson
, Jose L. Rodrigo

Mathematics

Research output: Contribution to journal › Article › peer-review

180 Scopus citations

Abstract

This paper establishes the local-in-time existence and uniqueness of strong solutions in H^s 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].

Original language	English (US)
Pages (from-to)	1035-1056
Number of pages	22
Journal	Journal of Functional Analysis
Volume	267
Issue number	4
DOIs	https://doi.org/10.1016/j.jfa.2014.03.021
State	Published - Aug 15 2014

All Science Journal Classification (ASJC) codes

Analysis

Keywords

Commutator estimates
MHD
Magnetohydrodynamics

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10.1016/j.jfa.2014.03.021

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

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].",

keywords = "Commutator estimates, MHD, Magnetohydrodynamics",

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T1 - Higher order commutator estimates and local existence for the non-resistive MHD equations and related models

AU - Fefferman, Charles L.

AU - McCormick, David S.

AU - Robinson, James C.

AU - Rodrigo, Jose L.

PY - 2014/8/15

Y1 - 2014/8/15

N2 - 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].

AB - 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].

KW - Commutator estimates

KW - MHD

KW - Magnetohydrodynamics

UR - https://www.scopus.com/pages/publications/84902550185

UR - https://www.scopus.com/pages/publications/84902550185#tab=citedBy

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DO - 10.1016/j.jfa.2014.03.021

M3 - Article

AN - SCOPUS:84902550185

SN - 0022-1236

VL - 267

SP - 1035

EP - 1056

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 4

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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