The almost global existence to classical solution for a 3-D wave equation of nematic liquid-crystals

TL;DR

This paper proves that small initial data lead to solutions of a 3-D wave equation modeling nematic liquid crystals existing for a very long time, nearly globally, in three-dimensional space.

Contribution

It establishes almost global existence results for classical solutions to a 3-D wave equation modeling nematic liquid crystals with small initial data.

Findings

Solutions exist for a very long time with small initial data

Almost global existence is proven for the wave equation

The lifespan of solutions is extended significantly

Abstract

In this paper we obtain the wave equation modeling the nematic liquid-crystals in three space dimensions and study the lifespan of classical solution to Cauchy problem. The almost global existence to classical solution for small initial data will be presented.