Inviscid limit for the full viscous MHD system with critical axisymmetric initial data

Abstract

This 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  [Abidi H, Hmidi T, Keraani S. On the global well-posedness for the axisymmetric Euler equations. Math. Ann. 2010;347:15–41.], [Hassainia Z. On the global well-posedness of the 3D axisymmetric resistive MHD equations. Ann. Henri Poincaré. 2022;23:2877-2917], [Hmidi T, Zerguine M. Inviscid limit axisymmetric Navier–Stokes system. Differential and Integral Equations. 2009;22(11–12):1223–1246.]. Furthermore, strong convergence in the resolution spaces with a rate of convergence is also studied.

Keywords:

• Full viscous MHD system
• global well-posedness
• axisymmetric solutions
• critical Besov spaces
• paradifferential calculus
• inviscid limit

2020 MSCs:

• 76W05
• 76D05
• 35B33
• 35Q35
• 35B07

Acknowledgments

The authors would like to thank the referees for their fruitful comments.

Special thanks to Taoufik Hmidi, Associate Professor, at the University of Rennes 1, France for his valuable and useful discussions.

Disclosure statement

No potential conflict of interest was reported by the author(s).