On the global well-posedness of the 3D axisymmetric resistive MHD equations

Abstract

In this paper, we prove the global well-posedness for the three-dimensional magnetohydrodynamics (MHD) equations with zero viscosity and axisymmetric initial data. First, we analyze the problem corresponding to the Sobolev regularities $H^s\times H^{s-2}$, with $s>5/2$. Second, we address the same problem but for the Besov critical regularities $B_{p,1}^{3/p+1}\times B_{1,p}^{3/p-1}$, $2\le p\le \infty$. This case turns out to be more subtle as the Beale-Kato-Majda criterion is not known to be valid for rough regularities.

References in corpus (1)

• Global well-posedness for the Euler-Boussinesq system with axisymmetric data

Cited by in corpus (4)

• Damped Strichartz estimates and the incompressible Euler--Maxwell system
• Axisymmetric Incompressible Viscous Plasmas: Global Well-Posedness and Asymptotics
• Global well-posedness for the non-viscous MHD equations with magnetic diffusion in critical Besov spaces
• Large amplitude traveling waves for the non-resistive MHD system