### 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 language | English (US) |
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Pages (from-to) | 322-333 |

Number of pages | 12 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 62 |

Issue number | 3 |

DOIs | |

State | Published - Mar 2009 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*62*(3), 322-333. https://doi.org/10.1002/cpa.20248

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

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 62, no. 3, pp. 322-333. https://doi.org/10.1002/cpa.20248

}

TY - JOUR

T1 - A simple justification of the singular limit for equatorial shallow-water dynamics

AU - Dutrifoy, Alexandre

AU - Majda, Andrew J.

AU - Schochet, Steven

PY - 2009/3

Y1 - 2009/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=61849139451&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=61849139451&partnerID=8YFLogxK

U2 - 10.1002/cpa.20248

DO - 10.1002/cpa.20248

M3 - Article

VL - 62

SP - 322

EP - 333

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 3

ER -