Year: 2026
Type: preprint
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 $L^1$.
Source: arXiv (Cornell University)
Author: Guelmame, Billel
Institution: New York University Abu Dhabi
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212033816