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


Ontology type: schema:ScholarlyArticle     


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

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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