Electron. J. Diff. Equ.,
Vol. 2013 (2013), No. 107, pp. 122.
Serrin blowup criterion for strong solutions to the 3D
compressible nematic liquid crystal flows with vacuum
Qiao Liu
Abstract:
In this article, we extend the wellknown Serrin's blowup criterion
for solutions of the 3D incompressible NavierStokes equations to
the 3D compressible nematic liquid crystal flows where the initial
vacuum is allowed. It is proved that for the initialboundary value
problem of the 3D 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; blowup criterion;
compressible NavierStokes equations.
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Qiao Liu
College of Mathematics and Computer Science
Hunan Normal University, Changsha
Hunan 410081, China
email: liuqao2005@163.com

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