Refined wave breaking for the one-dimensional nonlinear shallow water equations
Analysis of PDEs
2026-02-26 v1
Abstract
This paper aims to give a refined wave breaking description of the Cauchy problem to the one-dimensional nonlinear shallow water equations providing a sharp estimate of the lifespan of the solutions depending on the amplitude and topography parameters, under a non-cavitation condition which excludes the scenario that the solutions have compact support. We construct smooth initial data with finite -norm such that the -norm of the spatial derivative of the solution blows up at one single point in finite time with a precise blowup profile.
Cite
@article{arxiv.2602.21561,
title = {Refined wave breaking for the one-dimensional nonlinear shallow water equations},
author = {Pingchun Liu and Jean-Claude Saut and Shihan Sun and Yuexun Wang},
journal= {arXiv preprint arXiv:2602.21561},
year = {2026}
}
Comments
31 pages