Solvability of the Initial Value Problem to the Isobe–Kakinuma Model for Water Waves

Ryo Nemoto, Tatsuo Iguchi

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider the initial value problem to the Isobe–Kakinuma model for water waves and the structure of the model. The Isobe–Kakinuma model is the Euler–Lagrange equations for an approximate Lagrangian which is derived from Luke’s Lagrangian for water waves by approximating the velocity potential in the Lagrangian. The Isobe–Kakinuma model is a system of second order partial differential equations and is classified into a system of nonlinear dispersive equations. Since the hypersurface t= 0 is characteristic for the Isobe–Kakinuma model, the initial data have to be restricted in an infinite dimensional manifold for the existence of the solution. Under this necessary condition and a sign condition, which corresponds to a generalized Rayleigh–Taylor sign condition for water waves, on the initial data, we show that the initial value problem is solvable locally in time in Sobolev spaces. We also discuss the linear dispersion relation to the model.

Original languageEnglish
Pages (from-to)631-653
Number of pages23
JournalJournal of Mathematical Fluid Mechanics
Volume20
Issue number2
DOIs
Publication statusPublished - 2018 Jun 1

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water waves
Initial value problems
Water waves
Water Waves
boundary value problems
Initial Value Problem
Solvability
Nonlinear Dispersive Equations
Sobolev space
Model
Sobolev spaces
Linear Relation
Euler-Lagrange Equations
Dispersion Relation
Second order differential equation
partial differential equations
Sobolev Spaces
Partial differential equations
nonlinear equations
Hypersurface

ASJC Scopus subject areas

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics

Cite this

Solvability of the Initial Value Problem to the Isobe–Kakinuma Model for Water Waves. / Nemoto, Ryo; Iguchi, Tatsuo.

In: Journal of Mathematical Fluid Mechanics, Vol. 20, No. 2, 01.06.2018, p. 631-653.

Research output: Contribution to journalArticle

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