Blow up criterion for compressible nematic liquid crystal flows in dimension three

Abstract

In this paper, we consider the short time strong solution to a simplified hydrodynamic flow modeling the compressible, nematic liquid crystal materials in dimension three. We establish a criterion for possible breakdown of such solutions at finite time in terms of the temporal integral of both the maximum norm of the deformation tensor of velocity gradient and the square of maximum norm of gradient of liquid crystal director field.

22 pages

References in corpus (7)

• Blowup Criterion for the Compressible Flows with Vacuum States
• Blow up criterion for compressible nematic liquid crystal flows in dimension three
• A Beale-Kato-Majda Blow-up criterion for the 3-D compressible Navier-Stokes equations
• Strong solutions of the compressible nematic liquid crystal flow
• A blow-up criterion for the compressible liquid crystals system
• Serrin Type Criterion for the Three-Dimensional Viscous Compressible Flows
• Blow up criterion for nematic liquid crystal flows

Cited by in corpus (12)

• Recent developments of analysis for hydrodynamic flow of nematic liquid crystals
• Blow up criterion for compressible nematic liquid crystal flows in dimension three
• On Multi-dimensional Compressible Flows of Nematic Liquid Crystals with Large Initial Energy in a Bounded Domain
• Global solution to the three-dimensional compressible flow of liquid crystals
• Global Well-Posedness with Large Oscillations and Vacuum to the Three-Dimensional Equations of Compressible Nematic Liquid Crystal Flows
• Long-time Behavior of Solution for the Compressible Nematic Liquid Crystal Flows in ${\mathbb{R}}^3$
• Finite time blow-up for the nematic liquid crystal flow in dimension two
• Blow-up criterions of strong solutions to 3D compressible Navier-Stokes equations with vacuum
• The Optimal Decay Rate of Strong Solution for the Compressible Nematic Liquid Crystal Equations with Large Initial Data
• Global large solutions and incompressible limit for the compressible flow of liquid crystals
• Nonexistence of smooth solutions for the general compressible Ericksen -- Leslie equations in three dimensions
• Existence of global weak solutions to the compressible Ericksen-Leslie system in dimension one