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arXiv · 2505.23391

Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow

Niklas Knobel
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Abstract

We study the Sobolev stability thresholds of 2d dissipative fluid equations around Couette flow on the domain $\mathbb T\times \mathbb R$. We prove a bound for general nonlinear interactions, which, for several fluid equations, reduces the proof of nonlinear stability to a linear stability analysis. We apply this approach to the examples of Navier-Stokes, Boussinesq and magnetohydrodynamic equations around Couette flow. This improves the Sobolev stability threshold for the Boussinesq equations around Couette flow and large affine temperature to $1/3$ and for the MHD equations around Couette flow and constant magnetic field to $1/3^+$.

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Niklas Knobel. 2025-05-29. Suppression of Fluid Echoes and Sobolev Stability Threshold for 2D Dissipative Fluid Equations Around Couette Flow. https://arxiv.org/abs/2505.23391

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