On the global well-posedness of 3D axisymmetric MHD system with pure swirl magnetic field

2017/05/18 by Liu, Yanlin
#35Q30 #76D05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.06428

Abstract

In this paper, we consider the axisymmetric MHD system with nearly critical initial data having the special structure: u₀=u₀^r e_r+\ut₀ e_θ+u₀^z e_z, ~b₀=b₀^θe_θ. We prove that, this system is global well-posed provided the scaling-invariant norms ‖r\ut₀‖_L^∞,~‖r^-1 b^θ₀‖_L^\frac32 are sufficiently small.

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