Nonexistence of smooth solutions for the general compressible Ericksen -- Leslie equations in three dimensions

TL;DR

This paper proves that smooth solutions to the 3D compressible Ericksen--Leslie equations modeling nematic liquid crystal flow typically become non-smooth in finite time, indicating finite-time singularity formation.

Contribution

The paper establishes the finite-time blow-up of smooth solutions for the general compressible Ericksen--Leslie system in three dimensions, a significant advancement in understanding liquid crystal dynamics.

Findings

Smooth solutions generally lose regularity in finite time

Finite-time singularity formation is proven for the system

Results apply to the general 3D compressible Ericksen--Leslie equations

Abstract

We prove that the smooth solutions to the Cauchy problem for the compressible general three-dimensional Ericksen--Leslie system modeling nematic liquid crystal flow with conserved mass, linear momentum, and dissipating total energy, generally lose classical smoothness within a finite time.