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Autores principales: Liu, Ziran, Tran, Hung V., Yu, Yifeng
Formato: Preprint
Publicado: 2026
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Acceso en línea:https://arxiv.org/abs/2605.10478
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author Liu, Ziran
Tran, Hung V.
Yu, Yifeng
author_facet Liu, Ziran
Tran, Hung V.
Yu, Yifeng
contents For $\varepsilon>0$, let $ϕ^\varepsilon$ be the solution of the ergodic problem \[ \frac12 |Dϕ^\varepsilon|^2+F(x)-\varepsilonΔϕ^\varepsilon=c(\varepsilon) \qquad \text{on } \mathbb{T}^n, \] normalized by $ϕ^\varepsilon(0)=0$. We construct a one-dimensional example with $F\in C^3$ for which the vanishing-viscosity limit $\lim_{\varepsilon\to0}ϕ^\varepsilon$ does not exist. This gives a negative answer to a problem proposed by Jauslin, Kreiss, and Moser [10].
format Preprint
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institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Nonexistence of vanishing-viscosity limits for mechanical Hamiltonian ergodic problems
Liu, Ziran
Tran, Hung V.
Yu, Yifeng
Analysis of PDEs
For $\varepsilon>0$, let $ϕ^\varepsilon$ be the solution of the ergodic problem \[ \frac12 |Dϕ^\varepsilon|^2+F(x)-\varepsilonΔϕ^\varepsilon=c(\varepsilon) \qquad \text{on } \mathbb{T}^n, \] normalized by $ϕ^\varepsilon(0)=0$. We construct a one-dimensional example with $F\in C^3$ for which the vanishing-viscosity limit $\lim_{\varepsilon\to0}ϕ^\varepsilon$ does not exist. This gives a negative answer to a problem proposed by Jauslin, Kreiss, and Moser [10].
title Nonexistence of vanishing-viscosity limits for mechanical Hamiltonian ergodic problems
topic Analysis of PDEs
url https://arxiv.org/abs/2605.10478