This paper deals with the 3D incompressible nematic liquid crystal flows with density‐dependent viscosity in bounded domain. The global well‐posedness of strong solutions are established in the vacuum cases, provided the assumption that $\overline{\rho }+\Vert \nabla d_0{\Vert }_{L^3}$ is suitably small with large velocity. Furthermore, the exponential decay of the solution is also obtained.

中文翻译：

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具有密度依赖的粘度系数的3D不可压缩向列液晶流的整体适定性

本文讨论了在边界域中具有密度依赖性粘度的3D不可压缩向列液晶流。在真空情况下，可以确定强有力的解决方案在全球的适用性，前提是$\overline{\rho }+\Vert \nabla d_0{\Vert }_{{\mathrm{大号}}^3}$合适的是小而大的速度。此外，还获得了溶液的指数衰减。