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

Ping Zhang; Yuxi Zheng

doi:10.1002/cpa.20380

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

Ping Zhang, Yuxi Zheng

Mathematics

Research output: Contribution to journal › Article › peer-review

25 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 language	English (US)
Pages (from-to)	683-726
Number of pages	44
Journal	Communications on Pure and Applied Mathematics
Volume	65
Issue number	5
DOIs	https://doi.org/10.1002/cpa.20380
State	Published - May 2012

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

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10.1002/cpa.20380

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title = "Energy conservative solutions to a one-dimensional full variational wave system",

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.",

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AB - 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.

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

Abstract

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