Conservative solutions to a system of variational wave equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Hu, Yanbo^1,2 

[1] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China

[2] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

关键词: Variational wave equations;    Weak solutions;    Conservative solutions;   

DOI  :  10.1016/j.jde.2011.11.022

来源: Elsevier

【 摘 要 】

We investigate a system of variational wave equations which is the Euler-Lagrange equations of a variational principle arising in the theory of nematic liquid crystals and a few other physical contexts. We establish the global existence of an energy-conservative weak solution to its Cauchy problem for initial data of finite energy. The main difficulty arises from the possible concentration of energy. We construct the solution by introducing a new set of variables depending on the energy, whereby all singularities are resolved. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free