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An L5/6 bound for the periodic Kuramoto-Sivashinsky equation
Abstract
We consider the Kuramoto-Sivashinsky equation ut+uux+uxx+uxxxx=0 with L-periodic boundary conditions and zero spatial mean. We prove that every smooth solution satisfies |u(t)|L2≤ CL5/6+CL3/2/t for t>0, where C is a universal constant. In particular, |u(t)|L2≤ CL5/6 for all t≥ L2/3, independently of the initial norm.
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BibTeX
@misc{ingimarson2026bound,
title = {{An $L^5/6$ bound for the periodic Kuramoto-Sivashinsky equation}},
author = {Benjamin Ingimarson and Igor Kukavica and Qi Xu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04134},
eprint = {2611.04134},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04134},
}
RIS
TY - UNPB
TI - An L^5/6 bound for the periodic Kuramoto-Sivashinsky equation
AU - Benjamin Ingimarson
AU - Igor Kukavica
AU - Qi Xu
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04134
UR - https://arxiv.org/abs/2611.04134
AB - We consider the Kuramoto-Sivashinsky equation u_t+uu_x+u_xx+u_xxxx=0 with L-periodic boundary conditions and zero spatial mean. We prove that every smooth solution satisfies |u(t)|_L^2≤ CL^5/6+CL^3/2/t for t>0, where C is a universal constant. In particular, |u(t)|_L^2≤ CL^5/6 for all t≥ L^2/3, independently of the initial norm.
ER -