Nonexistence of subcritical solitary waves

Vladimir Kozlov, Evgeniy Lokharu, Miles H. Wheeler

Research output: Contribution to journalArticlepeer-review

Abstract

We prove the nonexistence of two-dimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open problem, and even in the irrotational case there are only partial results relying on sign conditions or smallness assumptions. As a corollary, we obtain a relatively complete classification of solitary waves: they must be supercritical, symmetric, and monotonically decreasing on either side of a central crest. The proof introduces a new function which is related to the so-called flow force and has several surprising properties. In addition to solitary waves, our nonexistence result applies to "half-solitary" waves (e.g. bores) which decay in only one direction.
Original languageEnglish
JournalArchive for Rational Mechanics and Analysis
Early online date17 May 2021
DOIs
Publication statusPublished - 17 May 2021

Keywords

  • water waves
  • solitary waves
  • Water waves with vorticity

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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