A NEW BLOWUP CRITERION FOR STRONG SOLUTIONS OF THE COMPRESSIBLE NEMATIC LIQUID CRYSTAL FLOW

摘要

In this paper, we establish a new blowup criterion for the strong solution to the simplified Ericksen-Leslie system modeling compressible nematic liquid crystal flows in a bounded domain Ω ⊂ R~3. Specifically, we obtain the blowup criterion in terms of ||P||L_t~∞BMO_ x and ||▽d||L_t~sL_x~∞, for any s > 3. The appearance of vacuum could be allowed.