Refined wave breaking for the one-dimensional nonlinear shallow water equations
Abstract
This paper aims to give a refined wave breaking description of the Cauchy problem for the one-dimensional nonlinear shallow water equations under a non-cavitation condition which excludes compactly supported water depth. We construct smooth, bounded initial data with first spatial derivatives in $ H^4(\mathbb R) $ such that the corresponding solution develops gradient blow-up at a single spatial point in finite time, and we give a precise description of the blow-up profile together with a quantitative estimate of the wave breaking time in terms of the initial compressive slope.
Fields of Study & Subjects
Advanced Mathematical Physics Problems
Nonlinear Waves and Solitons
Navier-Stokes equation solutions
Publication details
- Journal / source
- Discrete and Continuous Dynamical Systems
- Volume
- 60
- Issue
- 0
- Publication date
- 19 October 2026
- Language
- EN