@article{76fcd4820916488ea93c446f55ae49a4,
title = "Wave breaking in a shallow water model",
abstract = "We show wave breaking---bounded solutions with unbounded derivatives---in the nonlinear nonlocal equations which combine the dispersion relation of water waves and the nonlinear shallow water equations and which extend the Whitham equation to permit bidirectional propagation, provided that the slope of the initial data is sufficiently negative.",
keywords = "Blowup, Boussinesq, Shallow water, Wave breaking, Whitham",
author = "Hur, {Vera Mikyoung} and Lizheng Tao",
note = "Funding Information: The work of the first author was supported by National Science Foundation grant CAREER DMS-1352597, an Alfred P. Sloan Foundation fellowship, and a Beckman fellowship at the Center for Advanced Study at the University of Illinois at Urbana–Champaign. Funding Information: The work of the first author was supported by National Science Foundation grant CAREER DMS-1352597, an Alfred P. Sloan Foundation fellowship, and a Beckman fellowship at the Center for Advanced Study at the University of Illinois at Urbana?Champaign. Publisher Copyright: {\textcopyright} 2018 Society for Industrial and Applied Mathematics. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",
year = "2018",
doi = "10.1137/15M1053281",
language = "English (US)",
volume = "50",
pages = "354--380",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",
}