Vol. 10, No. 6, 2017

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Global well-posedness of the MHD equations in a homogeneous magnetic field

Dongyi Wei and Zhifei Zhang

Vol. 10 (2017), No. 6, 1361–1406
Abstract

We study the MHD equations with small viscosity and resistivity coefficients, which may be different. This is a typical setting in high temperature plasmas. It was proved that the MHD equations are globally well-posed if the initial velocity is close to 0 and the initial magnetic field is close to a homogeneous magnetic field in the weighted Hölder spaces. The main novelty is that the closeness is independent of the dissipation coefficients.

Keywords
MHD equations, global well-posedness, Hölder spaces
Mathematical Subject Classification 2010
Primary: 76W05
Milestones
Received: 20 September 2016
Revised: 31 March 2017
Accepted: 9 May 2017
Published: 14 July 2017
Authors
Dongyi Wei
School of Mathematical Sciences
Peking University
Beijing, 100871
China
Zhifei Zhang
School of Mathematical Sciences
Peking University
Beijing, 100871
China