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arXiv · 2401.12548

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

Niklas Knobel
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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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Niklas Knobel. 2024-01-23. Sobolev Stability for the 2D MHD Equations in the Non-Resistive Limit. https://arxiv.org/abs/2401.12548

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