Nonexistence of vanishing-viscosity limits for mechanical Hamiltonian ergodic problems

Ziran Liu, Hung V. Tran, Yifeng Yu

For $\epsilon >0$, let ${\varphi }^{\epsilon }$ be the solution of the ergodic problem \[ \frac12 |Dϕ^\varepsilon|^2+F(x)-\varepsilonΔϕ^\varepsilon=c(\varepsilon) \qquad \text{on } \mathb…