Lower Bounds for Advection-Diffusion Equations: An Exploration with AI-Generated Proofs
A new paper explores lower bounds for advection-diffusion equations using AI-generated proofs. The research presents explicit lower bounds in various settings, demonstrating the capabilities of AI in producing rigorous mathematical results. This study contributes to the field of analysis of partial differential equations and artificial intelligence.
- ▪The paper establishes explicit lower bounds for advection-diffusion equations in three different settings.
- ▪It includes a polynomial bound for inviscid shears and a uniform positive lower bound on the mixing scale for diffusive shears.
- ▪The proofs were generated entirely by an AI system called QED without human intervention.
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| Original publisher | arXiv cs.AI |
| Canonical URL | https://arxiv.org/abs/2605.20623 |
| Publication time | Fri, 22 May 2026 00:00:00 -0400 |
| Retrieval time | 2026-05-22T04:02:00.009Z |
| Last seen | 2026-05-22T04:02:00.009Z |
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| Commercial reuse | May the content be reused commercially? | Not permitted |
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Mathematics > Analysis of PDEs arXiv:2605.20623 (math) [Submitted on 20 May 2026] Title:Lower Bounds for Advection-Diffusion Equations: An Exploration with AI-Generated Proofs Authors:Chenyang An, Xiaoqian Xu View a PDF of the paper titled Lower Bounds for Advection-Diffusion Equations: An Exploration with AI-Generated Proofs, by Chenyang An and 1 other authors View PDF HTML (experimental) Abstract: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.
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