A model system for strong interaction between internal solitary waves View Full Text


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Article Info

DATE

1992-01

AUTHORS

Jerry L. Bona, Gustavo Ponce, Jean-Claude Saut, Michael M. Tom

ABSTRACT

A mathematical theory is mounted for a complex system of equations derived by Gear and Grimshaw that models the strong interaction of two-dimensional, long, internal gravity waves propagating on neighboring pycnoclines in a stratified fluid. For the model in question, the Cauchy problem is of interest, and is shown to be globally well-posed in suitably strong function spaces. Our results make use of Kato's theory for abstract evolution equations together with somewhat delicate estimates obtained using techniques from harmonic analysis. In weak function classes, a local existence theory is developed. The system is shown to be susceptible to the dispersive blow-up phenomenon investigated recently by Bona and Saut for Korteweg-de Vries-type equations. More... »

PAGES

287-313

References to SciGraph publications

  • 1979-01. On the Korteweg-de Vries equation in MANUSCRIPTA MATHEMATICA
  • 1976-03. Remarks on the Korteweg-de Vries equation in ISRAEL JOURNAL OF MATHEMATICS
  • 1988-03. Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf02099010

    DOI

    http://dx.doi.org/10.1007/bf02099010

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1006384439


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