Energy conservative solutions to a nonlinear   wave system of nematic liquid crystals

Geng Chen; Ping Zhang; Yuxi Zheng

doi:10.3934/cpaa.2013.12.1445

Article Contents

2013, Volume 12, Issue 3: 1445-1468. Doi: 10.3934/cpaa.2013.12.1445

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Energy conservative solutions to a nonlinear wave system of nematic liquid crystals

1.
Department of Mathematics, The Pennsylvania State University, University Park, PA 16802
2.
Academy of Mathematics & Systems Science, and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing 100190
3.
Department of Mathematical Sciences, Yeshiva University, New York, NY 10033

Received: February 29, 2012

Revised: March 31, 2012

Published: April 2013

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Abstract

We establish the global existence of solutions to the Cauchy problem for a system of hyperbolic partial differential equations in one space dimension modeling a type of nematic liquid crystals that has equal splay and twist coefficients. Our results have no restrictions on the angles of the director, as we use the director in its natural three-component form, rather than the two-component form of spherical angles.

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Mathematics Subject Classification: Primary: 35L65, 35J70; Secondary: 35J65.

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