On global well-posedness for a class of nonlocal dispersive wave equations
type: Item
instance of: scholarly article
title: On global well-posedness for a class of nonlocal dispersive wave equations
zbMATH Open document ID: 1117.35071
author: Luc Molinet
author: Francis Ribaud
published in: Discrete and Continuous Dynamical Systems
publication date: 2007-04-10T00:00:00Z
review text: The authors deal with the initial value problem for the following class of one-dimensional nonlocal dispersive wave equations \[ u_t+ D^{1+\alpha}_x\partial_x u+ uu_x= 0,\quad u(0)= u_0,\tag{1} \] where \(D^{1+\alpha}_x\) denotes the Fourier multiplier with symbols \(|\xi|^{1+\alpha}\), \(0\leq\alpha\leq 1\). The authors prove global well-posedness for (1) in Sobolev spaces with weighted low frequencies.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35R10
zbMATH DE Number: 5141169
zbMATH Keywords: wave equation
zbMATH Keywords: global existence
zbMATH Keywords: Bourgain spaces
zbMATH Keywords: Fourier multiplier
zbMATH Keywords: Sobolev spaces
MaRDI profile type: Publication
full work available at URL: dcds.2006.15.657
OpenAlex ID: W1970856119
DOI: 10.3934/DCDS.2006.15.657
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description: scientific article; zbMATH DE number 5141169