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

2025/05/29 by Niklas Knobel, Knobel, Niklas · 2 citations
Mathematics · Engineering · #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2505.23391

Abstract

We study the Sobolev stability thresholds of 2d dissipative fluid equations around Couette flow on the domain \mathbb T× \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⁺.

Cited by

• Stability threshold of the 2D Boussinesq system near Couette flow in an infinite channel
• Transition threshold for the Navier-Stokes-Coriolis system at high Reynolds numbers

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