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Global well-posedness and conservation laws for the water wave interaction equation

Published online by Cambridge University Press:  14 November 2011

Takayoshi Ogawa
Takayoshi Ogawa
Affiliation:
Department of Mathematics, University of California Santa Barbara, Santa Barbara, CA 93106, U.S.A.
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Abstract

Interaction equations of long and short water wave are considered. It is shown that the Cauchy problem for

is locally well posed in the largest space where the three conservations

can be justified. Here E(u,v) is the energy functional associated to the system. By these conservation laws, we establish the global well-posedness of the system in the largest class of initial data.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 127 , Issue 2 , 1997 , pp. 369 - 384
Copyright
Copyright © Royal Society of Edinburgh 1997

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