Une théorie trois-dimensionnelle des ondes de surface de l'eau et le développement de Friedrichs. II. (A three dimensional theory of surface waves of water and the expansion of Friedrichs. II.)
type: Item
instance of: scholarly article
title: Une théorie trois-dimensionnelle des ondes de surface de l'eau et le développement de Friedrichs. II. (A three dimensional theory of surface waves of water and the expansion of Friedrichs. II.)
zbMATH Open document ID: 0609.76013
author: Tadayoshi Kano
published in: Journal of Mathematics of Kyoto University
publication date: 1986-01-01T00:00:00Z
review text: [For part I see the review above (Zbl 0609.76012).] In this second part of the paper, the author derives the consequences of his own results obtained in the first part. He describes the expansion of the Cauchy problem solution on the free boundary, giving so a mathematical foundation for the three dimensional wave surface equations in a slight deeply water. The solution of the problem is also analytical with respect to \(\delta\), for every point in the movement domain, the expansion can be extended to a general three dimensional movement. A critical chapter, concerning the achievements and the limits of the paper, closes it.
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35R35
Mathematics Subject Classification ID: 35C20
Mathematics Subject Classification ID: 46N99
zbMATH DE Number: 3986848
zbMATH Keywords: surface waves
zbMATH Keywords: Cauchy problem
zbMATH Keywords: free boundary
zbMATH Keywords: three dimensional wave surface equations
zbMATH Keywords: slight deeply water
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520915
OpenAlex ID: W1561556815
DOI: 10.1215/KJM/1250520915
description: scientific article; zbMATH DE number 3986848