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Large norm inflation of the current in the viscous, non-resistive magnetohydrodynamics equations

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arxiv 2410.22804 v1 pith:IBBMUVQL submitted 2024-10-30 math.AP

Michele Dolce , Niklas Knobel , Christian Zillinger This is my paper
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keywords equationscurrentinflationlargemagneticmagnetohydrodynamicsnormviscous
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We consider the ideally conducting, viscous magnetohydrodynamics (MHD) equations in two dimensions. Specifically, we study the nonlinear dynamics near a combination of Couette flow and a constant magnetic field in a periodic infinite channel. In contrast to the Navier-Stokes equations this system is shown to exhibit algebraic instability and large norm inflation of the magnetic current on non-perturbative time scales.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  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.

  2. Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow

    math.AP 2025-05 conditional novelty 6.0 of 10

    A unified nonlinear estimate suppresses fluid echoes and reduces the Sobolev stability threshold for 2D Boussinesq and MHD Couette flow from 1/2 to 1/3, with a logarithmic correction for MHD.

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