Large scale behavior in the Kuramoto-Sivashinsky equation: The Schwinger-Dyson route

Olivier Coquand

Large scale behavior in the Kuramoto-Sivashinsky equation: The Schwinger-Dyson route

Statistical Mechanics 2026-07-20 v1 Chaotic Dynamics Fluid Dynamics

Authors: Olivier Coquand

Abstract

The present paper is a study of the large scale properties of the Kuramoto-Sivashinsky equation. By using a Schwinger-Dyson framework, we aim to provide a proof that the only solutions that can sustain a stable scaling in the infrared limit have a negative effective viscosity (in the Kuramoto-Sivashinsky sense) with a minimal set of hypotheses, thereby showing that this constitutes a general property of the wave equation that does not depend on a specific set of truncations of a renormalisation group flow, or limitations of a given numerical scheme for example.

Keywords

Kuramoto-Sivashinsky equation large scale behavior Schwinger-Dyson equations effective viscosity infrared limit turbulence

Cite

@article{arxiv.2607.17915,
  title  = {Large scale behavior in the Kuramoto-Sivashinsky equation: The Schwinger-Dyson route},
  author = {Olivier Coquand},
  journal= {arXiv preprint arXiv:2607.17915},
  year   = {2026}
}

Comments

12 pages, 2 figures