The stability threshold for 2D MHD equations around Couette with general viscosity and magnetic resistivity

2024/10/27 by Fei Wang, Wang, Fei, Zeren Zhang +1 · 2 citations
Mathematics · Engineering · #Navier-Stokes equation solutions #Advanced Mathematical Physics Problems #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.2410.20404

Abstract

We address a threshold problem of the Couette flow (y,0) in a uniform magnetic field (β,0) for the 2D MHD equation on \mathbbT×ℝ with fluid viscosity ν and magnetic resistivity μ. The nonlinear enhanced dissipation and inviscid damping are also established. In particularly, when 0<ν≤μ³≤1, we get a threshold ν^(1)/(2)μ^(1)/(3) in H^N(N≥4). When 0<μ³≤ν≤1, we obtain a threshold min\ν^(1)/(2),μ^(1)/(2)\min\1,ν^-1μ^(1)/(3)\, hence improving the results in [19,14,21].

Cited by

• Stability threshold of the 2D Boussinesq system near Couette flow in an infinite channel
• Nonlinear instability for the 3D MHD equations around the Taylor-Couette flow

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