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

Takayoshi Ogawa

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

Interaction equations of long and short water wave are considered. It is shown that the Cauchy problem for (Equation Presented) is locally well posed in the largest space where the three conservations ∥u(t)∥2 = ∥u0∥∥2, ∥ν(t)∥22 + 2 Im ∫ u(t)∂xū(t) dx = ∥ν022 + 2 Im ∫ u0xū0 dx, E(u(t), ν(t)) = E(u0, ν0) can be justified. Here E(u, ν) 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.

Original languageEnglish
Pages (from-to)369-384
Number of pages16
JournalRoyal Society of Edinburgh - Proceedings A
Volume127
Issue number2
DOIs
Publication statusPublished - 1997 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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