English

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 L2L^2 norm of spatial mean-free solutions to the advection--diffusion equation on T2\mathbb{T}^2 with shear drifts satisfies an \emph{exponential lower bound} in time. This lower bound shows that diffusion can fundamentally suppress passive-scalar mixing.

Keywords

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}
}
R2 v1 2026-07-01T07:43:15.191Z