Work

Anomalous Dissipation Via Spontaneous Stochasticity With a Two-dimensional Autonomous Velocity Field

Year: 2026

Type: article

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.

Source: Duke Mathematical Journal

DOI: 10.1215/00127094-2025-0067

Authors: Carl Johan Peter Johansson, Massimo Sorella

Institutions: École Polytechnique Fédérale de Lausanne, Imperial College London

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Staatssekretariat für Bildung, Forschung und Innovation

Award: G2250497198