On the vanishing viscosity limit for the full viscous MHD system with critical axisymmetric initial data

TL;DR

This paper proves the global existence and convergence of solutions for the viscous MHD system with axisymmetric initial data, maintaining uniformity across viscosity parameters in critical Besov spaces.

Contribution

It establishes the global well-posedness and strong convergence results for the viscous MHD equations in critical Besov spaces, with uniformity in viscosity.

Findings

Global solutions exist in critical Besov spaces.

Solutions converge strongly with a quantifiable rate.

Results are uniform with respect to viscosity.

Abstract

The current paper establishes the global well-posedness issue for the full viscous MHD equations in the axisymmetric setting. Global solutions are obtained in critical Besov spaces uniformly to the viscosity when the resistivity is fixed in the spirit of \cite{AKH,Hassainia,hz0}. Furthermore, strong convergence in the resolution spaces with a rate of convergence is also studied.