Transition Threshold for Strictly Monotone Shear Flows in Sobolev Spaces

2024/09/13 by Beekie, Rajendra, He, Siming · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.09219

Abstract

We study the stability of spectrally stable, strictly monotone, smooth shear flows in the 2D Navier-Stokes equations on \mathbbT × ℝ with small viscosity ν. We establish nonlinear stability in H^s for s ≥ 2 with a threshold of size εν^1/3 for time smaller than c_*ν^-1 with ε, c_* ≪ 1. Additionally, we demonstrate nonlinear inviscid damping and enhanced dissipation.

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• Stability of Stochastically Driven Couette Flow in 2D with Navier Boundary Conditions at high Reynolds number via Averaging Principle

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