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Sobolev Stability for the 2D MHD Equations in the Non-Resistive Limit

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arxiv 2401.12548 v1 pith:ZT2NJPJI submitted 2024-01-23 math.AP math-phmath.MP

classification math.APmath-phmath.MP
keywords kappastabilityconsiderequationslimitsobolevarticlebound
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abstract

In this article, we consider the stability of the 2D magnetohydrodynamics (MHD) equations close to a combination of Couette flow and a constant magnetic field. We consider the ideal conductor limit for the case when viscosity $\nu$ is larger than resistivity $\kappa$, $\nu\ge \kappa>0$. For this regime, we establish a bound on the Sobolev stability threshold. Furthermore, for $\kappa\le \nu^3$ this system exhibits instability, which leads to norm inflation of size $\nu \kappa^{-\frac 1 3 }$.

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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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