PreprintCC0arXiv
On the singular limit of the Camassa-Holm equation
Abstract
We study the singular limit of the Camassa--Holm equation as the length scale ℓ tends to zero. Although the formal limit is the Burgers equation with flux 3u2/2, we show that, for a class of smooth initial data, convergence to entropy solutions fails after the shock formation, even along subsequences in local space-time L1.
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BibTeX
@misc{guelmame2026singular,
title = {{On the singular limit of the Camassa-Holm equation}},
author = {Billel Guelmame},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08227},
eprint = {2609.08227},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08227},
note = {CC0},
}
RIS
TY - UNPB
TI - On the singular limit of the Camassa-Holm equation
AU - Billel Guelmame
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08227
UR - https://arxiv.org/abs/2609.08227
AB - We study the singular limit of the Camassa--Holm equation as the length scale ℓ tends to zero. Although the formal limit is the Burgers equation with flux 3u^2/2, we show that, for a class of smooth initial data, convergence to entropy solutions fails after the shock formation, even along subsequences in local space-time L^1.
ER -