Lower Bounds for Advection-Diffusion Equations: An Exploration with AI-Generated Proofs
We establish explicit lower bounds for advection-diffusion equations in three settings: a polynomial $\dot H^{-1}$ bound for inviscid shears with $u\in L^\infty_t W^{1,1}_y$, 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.
| Authors | Chenyang An, Xiaoqian Xu |
|---|---|
| Primary category | math.AP |
| Published | 20 May 2026 |
| Last updated at source | 20 May 2026 |
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