ANOMALOUS DISSIPATION VIA SPONTANEOUS STOCHASTICITY WITH A TWO-DIMENSIONAL AUTONOMOUS VELOCITY FIELD
Abstract
We study anomalous dissipation in the context of passive scalars and we construct a two-dimensional autonomous divergence-free velocity field in Cα (with α∈(0,1) arbitrary but fixed) which exhibits anomalous dissipation. Our proof employs the fluctuation-dissipation formula, which links spontaneous stochasticity with anomalous dissipation. Therefore, we address the issue of anomalous dissipation by showing that the variance of stochastic trajectories, in the zero noise limit, remains positive. Based on this result, we answer Questions 2.2 and Question 2.3 in Bruè and De Lellis regarding anomalous dissipation for the forced three-dimensional Navier–Stokes equations.
Fields of Study & Subjects
Advanced Thermodynamics and Statistical Mechanics
Complex Systems and Time Series Analysis
Publication details
- Journal / source
- Duke Mathematical Journal
- Publisher
- Duke University Press
- Volume
- 175
- Issue
- 11
- Pages
- 1957–2024
- Publication date
- 31 July 2026
- Language
- EN