Low regularity global well-posedness of axisymmetric MHD equations with vertical dissipation and magnetic diffusion

TL;DR

This paper proves the global existence and uniqueness of low-regularity solutions for 3D axisymmetric MHD equations with vertical dissipation and magnetic diffusion, using advanced energy estimates and interpolation techniques.

Contribution

It establishes the first low-regularity global well-posedness results for this class of MHD equations with minimal dissipation assumptions.

Findings

Existence of unique global solutions with initial data in Lorentz spaces.

Use of higher-order energy estimates and real interpolation methods.

Results applicable to axisymmetric MHD systems with vertical dissipation.

Abstract

Consideration in this paper is the global well-posedness for the 3D axisymmetric MHD equations with only vertical dissipation and vertical magnetic diffusion. The existence of unique low-regularity global solutions of the system with initial data in Lorentz spaces is established by using higher-order energy estimates and real interpolation method.