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

2024/01/23 by Niklas Knobel, Knobel, Niklas · 1 citation
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.2401.12548

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 ν is larger than resistivity κ, ν≥ κ>0. For this regime, we establish a bound on the Sobolev stability threshold. Furthermore, for κ≤ ν³ this system exhibits instability, which leads to norm inflation of size νκ^{-\frac 1 3} .

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