Global Well-posedness for the Three Dimensional Simplified Inertial Ericksen-Leslie Systems Near Equilibrium

TL;DR

This paper proves the global existence of classical solutions for a simplified inertial Ericksen-Leslie system modeling nematic liquid crystal flow, coupling Navier-Stokes and wave map equations, near equilibrium.

Contribution

It establishes the first global well-posedness result for this simplified inertial system close to equilibrium.

Findings

Global classical solutions exist near equilibrium.

The system remains well-posed over time.

Coupling Navier-Stokes with wave maps is effectively handled.

Abstract

We study a simplified inertial Ericksen-Leslie system for the nematic liquid crystal flow, which can be viewed as a system coupling Navier-Stokes equations and wave map equations. We prove the global existence of classical solution with initial data near equilibrium.