Global Low-Energy Weak Solution and Large-Time Behavior for the Compressible Flow of Liquid Crystals

Abstract

We consider the weak solution of the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in ${\mathbb{R}}^3$. When the initial data is small in $L^2$ and initial density is positive and essentially bounded, we first prove the existence of a global weak solution in ${\mathbb{R}}^3$. The large-time behavior of a global weak solution is also established.

arXiv admin note: text overlap with arXiv:1110.0053, arXiv:1004.4749 by other authors

References in corpus (1)

• Global Well-Posedness with Large Oscillations and Vacuum to the Three-Dimensional Equations of Compressible Nematic Liquid Crystal Flows