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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.20623 |
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| _version_ | 1866916030722342912 |
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| author | An, Chenyang Xu, Xiaoqian |
| author_facet | An, Chenyang Xu, Xiaoqian |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20623 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lower Bounds for Advection-Diffusion Equations: An Exploration with AI-Generated Proofs An, Chenyang Xu, Xiaoqian Analysis of PDEs Artificial Intelligence 35Q35 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. |
| title | Lower Bounds for Advection-Diffusion Equations: An Exploration with AI-Generated Proofs |
| topic | Analysis of PDEs Artificial Intelligence 35Q35 |
| url | https://arxiv.org/abs/2605.20623 |