Well-Posedness for the Boussinesq-Type System Related to the Water Wave

Naoyasu Kita, Jun Ichi Segata

研究成果: Contribution to journalArticle

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This paper studies the initial value problem of Boussinesq-type system which describes the motion of water waves. We show the time local well-posedness in the weighted Sobolev space. This is the generalization of Angulo’s work [1] from the view of regularity. Our argument is based on the contraction mapping principle for the integral equations after reducing our problem into the derivative nonlinear Schrödinger system. To overcome the regularity loss in the nonlinearity, we shall apply the smoothing effects of linear Schrödinger group due to Kenig-Ponce-Vega [7]. The gauge transform is also used to remove size restriction on the initial data.

元の言語英語
ページ(範囲)329-350
ページ数22
ジャーナルFunkcialaj Ekvacioj
47
発行部数2
DOI
出版物ステータス出版済み - 1 1 2004

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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