Algebraic calming for the 2D Kuramoto-Sivashinsky equations
Analysis of PDEs
2023-04-21 v1 Numerical Analysis
Numerical Analysis
Abstract
We propose an approximate model for the 2D Kuramoto-Sivashinsky equations (KSE) of flame fronts and crystal growth. We prove that this new ``calmed'' version of the KSE is globally well-posed, and moreover, its solutions converge to solutions of the KSE on the time interval of existence and uniqueness of the KSE at an algebraic rate. In addition, we provide simulations of the calmed KSE, illuminating its dynamics. These simulations also indicate that our analytical predictions of the convergence rates are sharp. We also discuss analogies with the 3D Navier-Stokes equations of fluid dynamics.
Cite
@article{arxiv.2304.10493,
title = {Algebraic calming for the 2D Kuramoto-Sivashinsky equations},
author = {Matthew Enlow and Adam Larios and Jiahong Wu},
journal= {arXiv preprint arXiv:2304.10493},
year = {2023}
}
Comments
35 pages, 8 figures