The Kuramoto-Sivashinsky Equation
Analysis of PDEs
2022-10-05 v1 Dynamical Systems
Chaotic Dynamics
Abstract
The Kuramoto-Sivashinsky equation was introduced as a simple 1-dimensional model of instabilities in flames, but it turned out to mathematically fascinating in its own right. One reason is that this equation is a simple model of Galilean-invariant chaos with an arrow of time. Starting from random initial conditions, manifestly time-asymmetric stripe-like patterns emerge. As we move forward in time, it appears that these stripes are born and merge, but do not die or split. We pose a precise conjecture to this effect, which requires a precise definition of 'stripes'.
Cite
@article{arxiv.2210.01711,
title = {The Kuramoto-Sivashinsky Equation},
author = {John C. Baez and Steve Huntsman and Cheyne Weis},
journal= {arXiv preprint arXiv:2210.01711},
year = {2022}
}
Comments
3 pages, 2 figures