Exponential Lower Bounds for the Advection-Diffusion Equation with Shear Flows
Analysis of PDEs
2025-12-23 v2
Abstract
In this paper, we prove that the norm of spatial mean-free solutions to the advection--diffusion equation on with shear drifts satisfies an \emph{exponential lower bound} in time. This lower bound shows that diffusion can fundamentally suppress passive-scalar mixing.
Cite
@article{arxiv.2511.14512,
title = {Exponential Lower Bounds for the Advection-Diffusion Equation with Shear Flows},
author = {Yupei Huang and Xiaoqian Xu},
journal= {arXiv preprint arXiv:2511.14512},
year = {2025}
}