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On the Cauchy problem of 3D nonhomogeneous incompressible nematic liquid crystal flows with vacuum

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    * Corresponding author
Yang Liu is supported by China Postdoctoral Science Foundation (No. 2018M642202) and National Natural Science Foundation of China (No. 11901288). Xin Zhong is supported by National Natural Science Foundation of China (No. 11901474)
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  • This paper deals with the Cauchy problem of three-dimensional (3D) nonhomogeneous incompressible nematic liquid crystal flows. The global well-posedness of strong solutions with large velocity is established provided that $ \|\rho_0\|_{L^\infty}+\|\nabla d_0\|_{L^3} $ is suitably small. In particular, the initial density may contain vacuum states and even have compact support. Furthermore, the large time behavior of the solution is also obtained.

    Mathematics Subject Classification: Primary: 35D35, 35Q35; Secondary: 76A15; 76D03.

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