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Transition Threshold for Strictly Monotone Shear Flows in Sobolev Spaces
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abstract
We study the stability of spectrally stable, strictly monotone, smooth shear flows in the 2D Navier-Stokes equations on $\mathbb{T} \times \mathbb{R}$ with small viscosity $\nu$. We establish nonlinear stability in $H^s$ for $s \geq 2$ with a threshold of size $\epsilon \nu^{1/3}$ for time smaller than $c_*\nu^{-1}$ with $\epsilon, c_* \ll 1$. Additionally, we demonstrate nonlinear inviscid damping and enhanced dissipation.
Forward citations
Cited by 2 Pith papers
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Stability threshold of Couette flow for 3D Boussinesq system in Sobolev spaces
For the 3D Boussinesq system near Couette flow with constant background temperature, H2 perturbations satisfying velocity and temperature smallness bounds of order ν and ν² respectively stay global in time.
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Enhanced Dissipation, Taylor Dispersion, and Inviscid Damping of Couette flow in the Boussinesq system on the Plane
A proof that Couette flow in the stably stratified Boussinesq system on R^2 is asymptotically stable for Richardson number R>1/4, with explicit enhanced dissipation, Taylor dispersion, and inviscid damping rates.
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