English

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 H˙5\dot{H}^5-norm such that the LL^\infty-norm of the spatial derivative of the solution blows up at one single point in finite time with a precise blowup profile.

Keywords

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

R2 v1 2026-07-01T10:51:15.080Z