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The Jauslin-Kreiss-Moser Vanishing-Viscosity Selection Problem

Differential equations · posed by Hans R. Jauslin, Heinz-Otto Kreiss, Jurgen Moser, 1999 · disproved

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Statement

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.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. construction · #1

    Ziran Liu, Hung V. Tran and Yifeng Yu, using ChatGPT

    That credit came with the record as it was imported. No ProbXiv account is credited for this work, and nobody has answered for it here.

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    ai assisted
    — a person led the work and used a model along the way.

    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.

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