On the singular limit of the Camassa-Holm equation

Billel Guelmame

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arXiv · 2609.08227

On the singular limit of the Camassa-Holm equation

Billel Guelmame

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Abstract

We study the singular limit of the Camassa--Holm equation as the length scale $\ell$ 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 $L^1$.

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Billel Guelmame. 2026-09-08. On the singular limit of the Camassa-Holm equation. https://arxiv.org/abs/2609.08227

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