Global Solution to a nonlinear wave equation of liquid crystal in the constant electric field

Linjun Huang

Global Solution to a nonlinear wave equation of liquid crystal in the constant electric field

Analysis of PDEs 2018-10-11 v2

Authors: Linjun Huang

Abstract

We construct a global conservative weak solution to the Cauchy problem for the non-linear variational wave equation $v_{tt} - c(v)(c(v)v_x)_x + \frac{1}{2}(v+v^3)= 0$ where $c(\cdot)$ is any smooth function with uniformly positive bounded value. This wave equation is derived from a wave system modelling nematic liquid crystals in a constant electric field.

Keywords

nonlinear wave equation liquid crystal constant electric field global weak solution cauchy problem conservative solution nematic

Cite

@article{arxiv.1806.05763,
  title  = {Global Solution to a nonlinear wave equation of liquid crystal in the constant electric field},
  author = {Linjun Huang},
  journal= {arXiv preprint arXiv:1806.05763},
  year   = {2018}
}

Comments

30 pages, 6 figures

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