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

Linjun Huang

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arXiv · 1806.05763

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

Linjun Huang

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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.

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Linjun Huang. 2018-06-14. Global Solution to a nonlinear wave equation of liquid crystal in the constant electric field. https://arxiv.org/abs/1806.05763

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