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

2018/06/14 by Linjun Huang, Huang, Linjun
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1806.05763

openalex publication_date 2018/06/14 · openalex created_date 2018/06/21 · openalex updated_date 2026/07/28

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 + (1)/(2)(v+v³)= 0 where c(⋅) 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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