Singularity for a multidimensional variational wave equation arising from nematic liquid crystals

2019/10/19 by Hu, Yanbo, Wang, Guodong
#35B44 #35L05 #35L72 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.08671

Abstract

This article is focused on a multidimensional nonlinear variational wave equation which is the Euler-Lagrange equation of a variational principle arising form the theory of nematic liquid crystals. By using the method of characteristics, we show that the smooth solutions for the spherically-symmetric variational wave equation breakdown in finite time, even for the arbitrarily small initial energy.

Related

• Singularity and existence to a wave system of nematic liquid crystals
• The almost global existence to classical solution for a 3-D wave equation of nematic liquid-crystals
• Global Solution to a nonlinear wave equation of liquid crystal in the constant electric field
• Singularity formation for the general Poiseuille flow of nematic liquid\n crystals
• Lipschitz optimal transport metric for a wave system modeling nematic liquid crystals