Global weak solution and large-time behavior for the compressible flow of liquid crystals

TL;DR

This paper proves the existence and analyzes the long-term behavior of global weak solutions for the three-dimensional compressible flow of liquid crystals with large initial data.

Contribution

It establishes the existence and large-time behavior of solutions for complex liquid crystal flow equations using a three-level approximation and energy estimates.

Findings

Existence of global weak solutions for the flow equations.

Large-time behavior characterized under certain conditions.

Applicable to large initial data in bounded domains.

Abstract

The three-dimensional equations for the compressible flow of liquid crystals are considered. An initial-boundary value problem is studied in a bounded domain with large data. The existence and large-time behavior of a global weak solution are established through a three-level approximation, energy estimates, and weak convergence for the adiabatic exponent $\gamma>\frac32$.