Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 107, pp. 1-22.

Title: Serrin blow-up criterion for strong solutions to the 3-D
       compressible nematic liquid crystal flows with vacuum
        
Author: Qiao Liu (Hunan Normal Univ., Changsha, Hunan, China)

Abstract:
  In this article, we extend the well-known Serrin's blow-up criterion
 for solutions of the 3-D incompressible Navier-Stokes equations to
 the 3-D compressible nematic liquid crystal flows where the initial
 vacuum is allowed. It is proved that for the initial-boundary value
 problem of the 3-D compressible nematic liquid crystal flows in a
 bounded domain, the strong solution exists globally if the velocity
 satisfies the Serrin's condition and $L^1(0,T;L^{\infty})$-norm of
 the gradient of the velocity is bounded.

Submitted September 12, 2012. Published April 24, 2013.
Math Subject Classifications: 76A15, 76N10, 35B65, 35Q35
Key Words: Compressible nematic liquid crystal flows; strong solution;
           Serrin's criterion; blow-up criterion; 
           compressible Navier-Stokes equations.