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摘要
In recent paper, we study the compressible biaxial nematic liquid crystal flow in a simply connected and smooth bounded domain omega subset of Double-struck capital R3$$ \Omega \subset {\mathbb{R}}<^>3 $$. An initial vacuum may exist in this flow. We firstly obtain a local existence of a unique strong solution by Galerkin's approximation method. Finally, we get a blow up criterion for such a local strong solution in terms of blow up of rho Lt infinity BMOx$$ {\left\Vert \rho \right\Vert}_{L_t<^>{\infty } BM{O}_x} $$ and backward difference nLtrLx infinity+ backward difference mLtrLx infinity$$ {\left\Vert \nabla n\right\Vert}_{L_t<^>r{L}_x<^>{\infty }}+{\left\Vert \nabla m\right\Vert}_{L_t<^>r{L}_x<^>{\infty }} $$ for any r>3$$ r>3 $$.
