Zero viscosity-resistivity limit for the 3D incompressible magnetohydrodynamic equations in Gevrey class

Fucai Li; Zhipeng Zhang

doi:10.3934/dcds.2018187

Article Contents

2018, Volume 38, Issue 9: 4279-4304. Doi: 10.3934/dcds.2018187

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Zero viscosity-resistivity limit for the 3D incompressible magnetohydrodynamic equations in Gevrey class

Fucai Li and
Zhipeng Zhang^,

Department of Mathematics, Nanjing University, Nanjing 210093, China

^* Corresponding author: Zhipeng Zhang
^* Corresponding author: Zhipeng Zhang

Received: May 2017

Revised: October 2017

Published: September 2018

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We study the zero viscosity-resistivity limit for the 3D incompressible magnetohydrodynamic (MHD) equations in a periodic domain in the framework of Gevrey class. We first prove that there exists an interval of time, independent of the viscosity coefficient and the resistivity coefficient, for the solutions to the viscous incompressible MHD equations. Then, based on these uniform estimates, we show that the solutions of the viscous incompressible MHD equations converge to that of the ideal incompressible MHD equations as the viscosity and resistivity coefficients go to zero. Moreover, the convergence rate is also given.

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Mathematics Subject Classification: Primary: 35Q30, 35Q35; Secondary: 76D03, 76D09.

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