Global existence of weak solution for the 2-D Ericksen-Leslie system

TL;DR

This paper establishes the global existence of weak solutions for the 2-D Ericksen-Leslie system with physical constraints, and proves local well-posedness in 2D and 3D, advancing mathematical understanding of liquid crystal models.

Contribution

It provides the first proof of global weak solutions for the 2-D Ericksen-Leslie system with Leslie and Ericksen stresses under physical constraints.

Findings

Global weak solutions exist for 2-D Ericksen-Leslie system.

Local well-posedness established in 2D and 3D.

Results hold under physical Leslie coefficient constraints.

Abstract

We prove the global existence of weak solution for two dimensional Ericksen-Leslie system with the Leslie stress and general Ericksen stress under the physical constrains on the Leslie coefficients. We also prove the local well-posedness of the Ericksen-Leslie system in two and three spatial dimensions.