Lower Bounds for Advection-Diffusion Equations: An Exploration with AI-Generated Proofs

arXiv:2605.20623v1 Announce Type: cross Abstract: We establish explicit lower bounds for advection-diffusion equations in three settings: a polynomial ot H^{-1} bound for inviscid shears with uin L^infty_t W^{1,1}_y, a uniform positive lower bound on the mixing scale for diffusive shears, and an exponential L^2 bound for rapidly oscillating time-periodic flows. All constants are explicit in the data. The proofs were generated entirely by a multi-agent math proving system, QED, without expert human intervention, serving as a test of AI's capability to produce rigorous mathematics.

Source: arXiv cs.AI | 2026-05-22