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

Takayoshi Ogawa

研究成果: Article査読

4 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)369-384
ページ数16
ジャーナルRoyal Society of Edinburgh - Proceedings A
127
2
DOI
出版ステータスPublished - 1997
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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