Weak solutions to a nonlinear variational wave equation with general data
type: Item
instance of: scholarly article
title: Weak solutions to a nonlinear variational wave equation with general data
zbMATH Open document ID: 1082.35129
author: Ping Zhang
author: Yuxi Zheng
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2005-05-04T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78654
review text: The global existence of weak solutions is established for an initial value problem for a nonlinear variational wave equation with rather general initial data, subject to the assumption that the wave speed satisfies certain conditions. High regularity is established for the spatial derivative \(\partial_x u\) of the wave amplitude \(u\). The wave equation arises from studies of nematic liquid crystals, of long waves on a dipole chain, and elsewhere. A high space-time estimate for \(\partial_x u\) is used to enable the case of possible concentrations to be considered.
reviewed by: Alan Jeffrey
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76A15
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 2165099
zbMATH Keywords: Existence
zbMATH Keywords: Regularity
zbMATH Keywords: Young measure
zbMATH Keywords: Wave equation
zbMATH Keywords: Renormalization
MaRDI profile type: Publication
OpenAlex ID: W1993649836
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DOI: 10.1016/J.ANIHPC.2004.04.001
description: scientific article; zbMATH DE number 2165099