Stability and inviscid limit of the 3D anisotropic MHD system near a background magnetic field with mixed fractional partial dissipation

2023/08/15 by Deng, Xuemin, Xiao, Yuelong, Zang, Aibin
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.07547

Abstract

A main result of this paper establishes the global stability of the three-dimensional MHD equations near a background magnetic field with mixed fractional partial dissipation with α, β∈((1)/(2), 1]. Namely, the velocity equations involve dissipation (Λ₁^2α + Λ₂^2α+σΛ₃^2α)u with the case σ=1 and σ=0. The magnetic equations without partial magnetic diffusion Λ_i^2β b_i but with the diffusion (-Δ)^βb, where Λ_i^s (s>0) with i=1, 2, 3 are the directional fractional operators. Then we focus on the vanishing vertical kinematic viscosity coefficient limit of the MHD system with the case σ=1 to the case σ=0. The convergent result is obtained in the sense of H¹-norm.

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