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

78 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

Access to Document

10.1016/j.jfa.2014.03.021

Fingerprint Dive into the research topics of 'Higher order commutator estimates and local existence for the non-resistive MHD equations and related models'. Together they form a unique fingerprint.

Cite this

@article{da27221476f7402d9c270668d75e83ec,

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",

author = "Fefferman, {Charles L.} and McCormick, {David S.} and Robinson, {James C.} and Rodrigo, {Jose L.}",

year = "2014",

month = aug,

day = "15",

doi = "10.1016/j.jfa.2014.03.021",

language = "English (US)",

volume = "267",

pages = "1035--1056",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "4",

}

TY - JOUR

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 - http://www.scopus.com/inward/record.url?scp=84902550185&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84902550185&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2014.03.021

DO - 10.1016/j.jfa.2014.03.021

M3 - Article

AN - SCOPUS:84902550185

VL - 267

SP - 1035

EP - 1056

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 4

ER -