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

Abstract

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.