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

Naoyasu Kita, Junichi Segata

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)329-350
Number of pages22
JournalFunkcialaj Ekvacioj
Volume47
Issue number2
DOIs
Publication statusPublished - Jan 1 2004

Fingerprint

Boussinesq System
Water Waves
Type Systems
Well-posedness
Regularity
Vega
Contraction Mapping Principle
Smoothing Effect
Local Well-posedness
Weighted Sobolev Spaces
Linear Group
Initial Value Problem
Gauge
Integral Equations
Nonlinear Systems
Nonlinearity
Transform
Restriction
Derivative
Motion

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Well-Posedness for the Boussinesq-Type System Related to the Water Wave. / Kita, Naoyasu; Segata, Junichi.

In: Funkcialaj Ekvacioj, Vol. 47, No. 2, 01.01.2004, p. 329-350.

Research output: Contribution to journalArticle

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