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A blow-up criterion for strong solutions to the compressible liquid crystals system. (Chinese. English summary) Zbl 1249.82030
Summary: The authors establish a blow-up criterion for strong solutions to the compressible liquid crystals equations in terms of the gradient of the velocity only, similar to Beale-Kato-Majda criterion for the ideal incompressible flows and the criterion obtained by X. Huang and Z. Xin [Sci. China, Math. 53, No. 3, 671–686 (2010; Zbl 1256.35059)] for the compressible Navier-Stokes equations. The energy law and a higher order energy inequality are employed to prove this criterion. The main difficulty stems from the vacuum at the initial time.

MSC:
82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35M10 PDEs of mixed type
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