Global well-posedness of the MHD equations in a homogeneous magnetic field

Wei, Dongyi; Zhang, Zhifei

doi:10.2140/apde.2017.10.1361

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Global well-posedness of the MHD equations in a homogeneous magnetic field

Dongyi Wei and Zhifei Zhang

Vol. 10 (2017), No. 6, 1361–1406

DOI: 10.2140/apde.2017.10.1361

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

Vol. 10, No. 6, 2017