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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
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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