Weak solutions to a nonlinear variational wave equation

Ping Zhang, Yuxi Zheng

Research output: Contribution to journalArticlepeer-review

41 Scopus citations

Abstract

We establish the global existence of weak solutions to the Cauchy problem for a nonlinear variational wave equation, where the wave speed is a given monotone function of the wave amplitude. The equation arises in modeling wave motions of nematic liquid crystals, long waves on a dipole chain, and a few other fields. We use the Young-measure method in the setting of Lp spaces. We overcome the difficulty that oscillations get amplified by the growth terms of the equation.

Original languageEnglish (US)
Pages (from-to)303-319
Number of pages17
JournalArchive for Rational Mechanics and Analysis
Volume166
Issue number4
DOIs
StatePublished - Mar 1 2003

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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