Optimal Linear Inviscid Damping and Vorticity Depletion for Non-monotonic shear flows

Abstract

We give a proof of optimal pointwise linear inviscid damping and vorticity depletion for a large class of spectrally stable shear flows $b(y)$ on the rectangular torus. This extends the linear inviscid estimates in \cite{CJWZ25} for Kolmogorov flow $b(y)=\cos y$ using completely different methods. Crucially, both methods remove an apparent logarithmic correction to the depletion and inviscid damping rates. Our method combines pointwise bounds for a parametrix with an explicit solution of a simpler inner problem which makes the removal of the logarithm clear.

arXiv comment58 pages