Existence of global weak solutions to the compressible Ericksen-Leslie system in dimension one

TL;DR

This paper proves the existence of global weak solutions for the one-dimensional compressible Ericksen-Leslie liquid crystal system with initial density conditions.

Contribution

It establishes the existence of global weak solutions for the compressible Ericksen-Leslie system in one dimension, expanding understanding of liquid crystal flow models.

Findings

Global weak solutions constructed for initial density in L^γ, γ>1

Solution existence proven for one-dimensional compressible liquid crystal flows

Advances mathematical understanding of liquid crystal dynamics

Abstract

We consider the compressible Ericksen-Leslie system of liquid crystal flows in one dimension. A global weak solution is constructed with initial density $\rho_0\geq 0$ and $\rho_0\in L^\gamma$ for $\gamma>1$.