Energy conservative solutions to a one-dimensional full variational wave system

Ping Zhang, Yuxi Zheng

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We establish the existence of a conservative weak solution to the initial value problem for a complete system of variational wave equations modeling liquid crystals in one space dimension, in which the director has two degrees of freedom. The solutions exist globally in time and singularities may develop in finite time, but the energy of the solutions is conserved across singular times. The method for existence also yields continuous dependence of solutions on the initial data.

Original languageEnglish (US)
Pages (from-to)683-726
Number of pages44
JournalCommunications on Pure and Applied Mathematics
Volume65
Issue number5
DOIs
StatePublished - May 1 2012

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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