AI 中文总结
本文证明了二维可压缩向列型液晶流在剪切粘度为常数、体粘度满足特定幂律且$\beta>4/3$时，无需限制初值大小且允许真空，强解全局存在且唯一，且初始取向场无需几何角度条件。
AI 中文摘要
本文研究全空间或半空间中二维可压缩向列型液晶流的全局适定性。在剪切粘度为正常数且体粘度为$\lambda(\rho)=\rho^\beta$（其中$\beta>4/3$）的假设下，我们建立了强解的全局存在性和唯一性。需要指出的是，我们的结果是在对初值大小没有任何限制的情况下获得的，并且允许真空的存在。特别地，初始取向场不需要满足任何几何角度条件。
英文摘要
This paper concerns the global well-posedness of two-dimensional compressible nematic liquid crystal flows in the whole space or in the half-space. Under the assumptions that the shear viscosity is a positive constant and that the bulk viscosity is given by $λ(ρ)=ρ^β$ with $β>4/3$, we establish the global existence and uniqueness of strong solutions. It should be mentioned that our results are obtained without any restrictions on the size of the initial data and allow for the presence of vacuum. In particular, the initial orientation field is not required to satisfy any geometric angle condition.
