Well-posedness of a highly nonlinear shallow water equation on the circle

Nilay Duruk Mutlubas, Anna Geyer, Ronald Quirchmayr

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

We present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literature review of all the available studies on this equation. Furthermore, we establish a novel result concerning the local well-posedness of the corresponding Cauchy problem for space-periodic solutions with initial data from the Sobolev space Hs on the circle for s>3∕2.

Original languageEnglish
Article number111849
JournalNonlinear Analysis, Theory, Methods and Applications
Volume197
DOIs
Publication statusPublished - 1 Aug 2020

Keywords

  • Cubic nonlinearity
  • Large amplitude waves
  • Shallow water equation
  • Well-posedness

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