Global Solution to a nonlinear wave equation of liquid crystal in the constant electric field
Abstract
We construct a global conservative weak solution to the Cauchy problem for the non-linear variational wave equation vtt - c(v)(c(v)vx)x + 12(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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