具大初值和真空的二维可压缩液晶流径向对称强解的整体适定性
Global well-posedness of radially symmetric strong solutions to two-dimensional compressible liquid crystal flows with large data and vacuum
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中文总结 AI 辅助
该研究针对具大初值和真空的二维可压缩液晶流径向对称强解，在β>1条件下建立其整体适定性，改进了相关研究结果，关键利用director径向对称性的刚性机制阻止集中现象。
中文摘要 AI 辅助
我们研究二维可压缩向列型液晶流的初边值问题，其中剪切粘度μ为正常数，体积粘度λ为密度的幂函数，幂指数为β。在β>1的条件下，我们建立了该Vaigant-Kazhikhov型模型（简化可压缩Ericksen-Leslie系统）在速度为Dirichlet边界条件、 director为Neumann边界条件下，具任意大初值和真空的径向对称强解的整体存在性及大时间行为。本工作改进了Zhong与Zhou（《Math. Ann.》第390卷，2024年；《J. Math. Pures Appl.》第212卷，2026年）针对一般二维区域的结果，移除了director的几何角度条件，并将β的约束从β>4/3放宽至β>1。关键在于director径向对称性产生的刚性机制可阻止输运调和热流中的集中现象。
英文摘要
We study the initial boundary value problem of the two-dimensional compressible nematic liquid crystal flow with the shear viscosity $μ$ being a positive constant and bulk viscosity $λ$ being a power function of density with the power exponent $β$. Under the condition $β>1$, we establish the global existence and large time behavior of the radially symmetric strong solutions to this Vaigant--Kazhikhov type model of simplified compressible Ericksen-Leslie system of Dirichlet boundary conditions for the velocity and Neumann boundary ones for the director with arbitrary large data and vacuum. This work improves the results of Zhong and Zhou (\textit{Math. Ann.} \textbf{390}, 2024; \textit{J. Math. Pures Appl.}, \textbf{212}, 2026) for general 2D domains by removing the geometric angel condition on the director and relaxing the constrain on $β$ from $β>4/3$ to $β>1$. The key ingredient is that the rigidity mechanism arising from the radial symmetry of director prevents concentration phenomena in the transported harmonic heat flow.
发表机构
- School of Mathematics and Statistics, Northwestern Polytechnical University（西北工业大学数学与统计学院）
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