发表机构
University of Chinese Academy of Sciences（中国科学院大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究二维非齐次不可压缩向列型液晶流，在密度依赖粘性下建立强解的全局存在性与指数衰减，并推广到常粘性大初始数据及柯西问题，无需几何角度条件。
AI 中文摘要
本文研究二维非齐次不可压缩向列型液晶流。对于允许初始密度为零的情形，我们首先在密度依赖粘性且有界区域中，假设对某个$q>2$，$\nabla \rho_0$的$L^q$范数足够小，建立了强解的全局存在性和指数衰减。作为推论，我们得到了常粘性情形下具有大初始数据的强解的全局存在性。此外，对于具有常粘性且远场密度为真空或非真空的柯西问题，我们证明了任意大初始数据下强解的全局存在性和长时间衰减速率。值得注意的是，我们的结果不要求初始取向场满足任何几何角度条件。
英文摘要
This paper studies the two-dimensional nonhomogeneous incompressible nematic liquid crystal flows with planar orientation fields taking values in $\mathbb{S}^1$. For the initial-boundary value problem in bounded domains with density-dependent viscosity, we establish the global existence and exponential decay of strong solutions with initial density allowing vacuum, provided that $\|\nabla μ(ρ_0)\|_{L^q}$ is sufficiently small for some $q>2$. The smallness condition is automatically satisfied when $μ$ is constant, and hence the result yields the global existence of strong solutions for arbitrarily large initial data in the constant viscosity case. Furthermore, for the Cauchy problem with constant viscosity and either vacuum or non-vacuum far-field density, we establish the global existence and large-time decay rates of strong solutions for arbitrarily large initial data. These results are obtained without imposing any geometric angle conditions on the initial orientation field.
