VibeMathedMath problems solved by AI
Sign in

The Jauslin-Kreiss-Moser Vanishing-Viscosity Selection Problem

For the ergodic problem 12∣Dφε∣2+F(x)−εΔφε=c(ε)\tfrac12|D\varphi^\varepsilon|^2 + F(x) - \varepsilon\Delta\varphi^\varepsilon = c(\varepsilon) on the torus, normalized by φε(0)=0\varphi^\varepsilon(0) = 0, Jauslin, Kreiss and Moser asked whether the vanishing-viscosity limit lim⁡ε→0φε\lim_{\varepsilon \to 0}\varphi^\varepsilon always exists. It need not: there is a one-dimensional example with F∈C3F \in C^3 for which the limit fails to exist.

Result
Disproved
Status
Resolved
AI contribution
AI-assisted
Method
Construction
Field
Hamilton-Jacobi equations
Posed by
Hans R. Jauslin, Heinz-Otto Kreiss, Jurgen Moser
Year posed
1999
Years open
27y
Solved
2026-05-11
Model
ChatGPT
Vendor
OpenAI
Collaborators
Ziran Liu, Hung V. Tran, Yifeng Yu
Verification
Unreviewed
Publication
Preprint
Significance
20 / 100
Disclosed cost
—
Wikipedia
No dedicated article

What the AI did

Generic rather than itemised, and prominent enough that the authors put it in the arXiv comment as well as the acknowledgement: they used ChatGPT during the development of the work, including for suggesting proof strategies and assisting with calculations, and then completed and rigorously checked every statement, proof and verification themselves. No model version is named and no individual step is attributed, which is what keeps this at the assistive end rather than higher.

Verification

arXiv preprint, not peer-reviewed. The result is an explicit one-dimensional counterexample built from local Dirichlet ground-state energies and a localization lemma, so it is checkable, but nobody independent has checked it.

Source

arXiv:2605.10478 - Nonexistence of vanishing-viscosity limits for mechanical Hamiltonian ergodic problems

Submitted by Curator34

Discussion