Global wellposedness and limit behavior for the generalized finite-depth-fluid equation with small data in critical Besov spaces \(\dot B^s_{2,1}\)
type: Item
instance of: scholarly article
title: Global wellposedness and limit behavior for the generalized finite-depth-fluid equation with small data in critical Besov spaces \(\dot B^s_{2,1}\)
zbMATH Open document ID: 1178.35302
author: LiJia Han
author: Baoxiang Wang
published in: Journal of Differential Equations
publication date: 2008-10-21T00:00:00Z
review text: In this very interesting and technical paper, the well known equation FDF (finite-depth-fluid) introduced by \textit{R. I. Joseph} [J. Physics A 10, L225--L227 (1977; Zbl 0369.76018)] is studied. For a suitable choice of some parameters and for small enough initial data, the globally wellpossedness is proved. Two convergence phenomena are also proved: for very large depth, the solution of FDF is converging to the solution of the generalized Korteweg-de Vries euqation and for small depth, the FDF solution is near the solution of Benjamin-Ono equation. The Kato smoothing effect for a dispersive semi-groups is used to obtain some estimates of the solution, useful for the convergence procedure. The dual estimate method and the oscillatory integral techniques are also used.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35B40
Mathematics Subject Classification ID: 76B03
zbMATH DE Number: 5354958
zbMATH Keywords: generalized-depth-fluid equation
zbMATH Keywords: Korteweg-de Vries equation
zbMATH Keywords: Benjamin-Ono equation
zbMATH Keywords: Cauchy problem
zbMATH Keywords: Besov spaces
reviewed by: Gelu Paşa
MaRDI profile type: Publication
full work available at URL: j.jde.2008.07.008
OpenAlex ID: W1991641024
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DOI: 10.1016/J.JDE.2008.07.008
description: scientific article; zbMATH DE number 5354958