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

Abstract

This paper is concerned with the three-dimensional equations of a simplified hydrodynamic flow modeling the motion of compressible, nematic liquid crystal materials. The authors establish the global existence of classical solution to the Cauchy problem with smooth initial data which are of small energy but possibly large oscillations with constant state as far-field condition which could be either vacuum or non-vacuum. The initial density is allowed to vanish and the spatial measure of the set of vacuum can be arbitrarily large, in particular, the initial density can even have compact support. As a byproduct, the large-time behavior of the solution is also studied.

arXiv comment46pages. arXiv admin note: text overlap with arXiv:1104.5685 and arXiv:1104.5684

References in corpus (5)

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• A blow-up criterion for the compressible liquid crystals system
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Cited by in corpus (6)

• Recent developments of analysis for hydrodynamic flow of nematic liquid crystals
• On Multi-dimensional Compressible Flows of Nematic Liquid Crystals with Large Initial Energy in a Bounded Domain
• Global Low-Energy Weak Solution and Large-Time Behavior for the Compressible Flow of Liquid Crystals
• Global finite energy weak solutions to the compressible nematic liquid crystal flow in dimension three
• Global Weak Solutions to the Equations of Compressible Flow of Nematic Liquid Crystals in Two Dimensions
• Incompressible Limit of the Compressible Nematic Liquid Crystal Flow