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2017 Global well-posedness of the MHD equations in a homogeneous magnetic field
Dongyi Wei, Zhifei Zhang
Anal. PDE 10(6): 1361-1406 (2017). 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.

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Dongyi Wei. Zhifei Zhang. "Global well-posedness of the MHD equations in a homogeneous magnetic field." Anal. PDE 10 (6) 1361 - 1406, 2017. https://doi.org/10.2140/apde.2017.10.1361

Information

Received: 20 September 2016; Revised: 31 March 2017; Accepted: 9 May 2017; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1368.76077
MathSciNet: MR3678491
Digital Object Identifier: 10.2140/apde.2017.10.1361

Subjects:
Primary: 76W05

Keywords: global well-posedness , Hölder spaces , MHD equations

Rights: Copyright © 2017 Mathematical Sciences Publishers

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