AI 中文总结
本文证明二维可压缩向列型液晶流在允许真空和大初值下强解全局存在唯一，并建立密度上界及向平衡态的指数衰减。
AI 中文摘要
本文研究了周期域或有界单连通域中二维可压缩向列型液晶流的强解的全局存在性与大时间行为。假设剪切粘度为正常数，而体积粘度由$\lambda(\rho)=\rho^\beta$给出，其中$\beta>4/3$。对于允许真空的初值，我们在不限制初值大小的情况下建立了强解的全局存在性和唯一性。特别地，对初始取向场不施加任何几何角度条件。此外，我们推导了密度的时间一致上界，并建立了强解向平衡态的指数衰减。
英文摘要
In this paper, we investigate the global existence and large-time behavior of strong solutions to two-dimensional compressible nematic liquid crystal flows in the periodic domain or in a bounded simply connected domain. The shear viscosity is assumed to be a positive constant, while the bulk viscosity is given by $λ(ρ)=ρ^β$ with $β>4/3$. For initial data allowing vacuum, we establish the global existence and uniqueness of strong solutions without any restrictions on the size of the initial data. In particular, no geometric angle condition is imposed on the initial orientation field. Moreover, we derive a time-uniform upper bound for the density and establish the exponential decay of the strong solutions toward equilibrium.
