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