Communications in Mathematical Sciences

Volume 19 (2021)

Number 7

Wave breaking for a model equation for shallow water waves of moderate amplitude

Pages: 1799 – 1807

DOI: https://dx.doi.org/10.4310/CMS.2021.v19.n7.a2

Author

Shaojie Yang (Department of Systems Science and Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan, China)

Abstract

This paper is devoted to studying wave breaking for a model equation for shallow water waves of moderate amplitude (also called the Constanin–Lannes equation), which was proposed by Constantin and Lannes. We first present a blow-up criterion and the precise blow-up scenario of strong solutions to the equation. Next, we show a sufficient condition on the initial data to guarantee wave breaking. Moreover, the estimate of life span is given. The key of the method is to refine the analysis on characteristics and conserved quantities to the Riccati-type differential inequality.

Keywords

wave breaking, shallow water waves of moderate amplitude, blow-up

2010 Mathematics Subject Classification

35G25, 35Q53

Full Text (PDF format)

This work was supported by the Yunnan Fundamental Research Projects (Grant No. KKSQ202107025).

Received 3 October 2019

Accepted 15 March 2021

Published 7 September 2021