Wave breaking in the Whitham equation

Research output: Contribution to journalArticlepeer-review

Abstract

We prove wave breaking — bounded solutions with unbounded derivatives — in the nonlinear nonlocal equation which combines the dispersion relation of water waves and a nonlinearity of the shallow water equations, provided that the slope of the initial datum is sufficiently negative, whereby we solve a Whitham's conjecture. We extend the result to equations of Korteweg–de Vries type for a range of fractional dispersion.

Original languageEnglish (US)
Pages (from-to)410-437
Number of pages28
JournalAdvances in Mathematics
Volume317
DOIs
StatePublished - Sep 7 2017

Keywords

  • Blow-up
  • Wave breaking
  • Whitham equation

ASJC Scopus subject areas

  • Mathematics(all)

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