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On the Sobolev Stability Threshold for the 2D MHD Equations with Horizontal Magnetic Dissipation

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arxiv 2309.00496 v1 pith:YCLLAMYE submitted 2023-09-01 math.AP math-phmath.MP

Niklas Knobel , Christian Zillinger This is my paper · ORCID
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keywords dissipationmagneticequationshorizontalregimestabilitythresholdarticle
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In this article we consider the stability threshold of the 2D magnetohydrodynamics (MHD) equations near a combination of Couette flow and large constant magnetic field. We study the partial dissipation regime with full viscous and only horizontal magnetic dissipation. In particular, we show that this regime behaves qualitatively differently than both the fully dissipative and the non-resistive setting.

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  1. The stability threshold for 3D MHD equations around Couette with rationally aligned magnetic field

    math.AP 2025-05 conditional novelty 7.0 of 10

    For 3D MHD with a rationally aligned background magnetic field, the sharp stability threshold around Couette flow is gamma=1, with inviscid damping and a nu^{-1/3} magnetic amplification.

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