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Asymptotic stability of two-dimensional Couette flow in a viscous fluid

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arxiv 2208.14898 v1 pith:JM5AE7OC submitted 2022-08-31 math.AP physics.flu-dyn

Hui Li , Nader Masmoudi , Weiren Zhao This is my paper · ORCID
classification math.APphysics.flu-dyn
keywords stabilityasymptoticbetanonlinearcouetteflowfracinitial
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abstract

In this paper, we study the nonlinear asymptotic stability of Couette flow for the two-dimensional Navier-Stokes equation with small viscosity $\nu>0$ in $\mathbb{T}\times\mathbb{R}$. It's generally known the nonlinear asymptotic stability of the Couette flow depends closely on the size and regularity of the initial perturbation, which yields the stability threshold problem. This work studies the relationship between the size and the regularity of the initial perturbation that makes the nonlinear asymptotic stability holds. More precisely, we proved that if the initial perturbation is in some Gevrey-$\frac{1}{s}$ class with size $\epsilon\nu^{\beta}$ where $s\geq \frac{1-3\beta}{2-3\beta}$ and $\beta\in [0,\frac{1}{3}]$, then the nonlinear asymptotic stability holds.

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Cited by 4 Pith papers

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

  1. Neutral curves and traveling waves in plane Poiseuille flow

    math.AP 2026-07 conditional novelty 7.0 of 10

    Rigorous proof that the lower and upper neutral branches of plane Poiseuille flow obey ν ~ α^7 and ν ~ α^11, with simple eigenvalues and transversal crossing, yielding traveling-wave bifurcation.

  2. 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.

  3. Improved stability threshold for 2D Navier-Stokes Couette flow in an infinite channel

    math.AP 2025-08 conditional novelty 6.0 of 10

    The ν^{1/2} stability threshold for 2D Navier-Stokes Couette flow in an infinite channel with Navier slip is proven, with no logarithmic loss, sharpening the Arbon-Bedrossian threshold.

  4. 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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