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

Alexandre Dutrifoy, Andrew J. Majda, Steven Schochet

Research output: Contribution to journalArticle

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

Fingerprint

Singular Limit
Froude number
Shallow Water
Justification
Parabolic Cylinder Functions
Symmetric Hyperbolic Systems
Shallow Water Equations
Wave equations
Variable Coefficients
Water
Wave equation
Tend
Converge
Series
Term
Generalization

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A simple justification of the singular limit for equatorial shallow-water dynamics. / Dutrifoy, Alexandre; Majda, Andrew J.; Schochet, Steven.

In: Communications on Pure and Applied Mathematics, Vol. 62, No. 3, 03.2009, p. 322-333.

Research output: Contribution to journalArticle

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