A simple justification of the singular limit for equatorial shallow-water dynamics

Alexandre Dutrifoy, Andrew J. Majda, Steven Schochet

Research output: Contribution to journalArticlepeer-review

Abstract

The equatorial shallow-water equations at low Froude number form a symmetric hyperbolic system with large variable-coefficient terms. Although such systems are not covered by the classical Klainerman-Majda theory of singular limits, the first two authors recently proved that solutions exist uniformly and converge to the solutions of the long-wave equations as the height and Froude number tend to 0. Their proof exploits the special structure of the equations by expanding solutions in series of parabolic cylinder functions. A simpler proof of a slight generalization is presented here in the spirit of the classical theory.

Original languageEnglish (US)
Pages (from-to)322-333
Number of pages12
JournalCommunications on Pure and Applied Mathematics
Volume62
Issue number3
DOIs
StatePublished - Mar 2009

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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