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 -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.
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| Qiao Liu |
College of Mathematics and Computer Science
Hunan Normal University, Changsha
Hunan 410081, China
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