On the Existence of Solutions to the Nematic Liquid Crystal Flow in Weak-Lp Spaces
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摘要: 本文关注高维不可压向列型液晶流方程的整体温和解的存在性问题. 本文证明了当初始值范数‖u0‖(n,∞)+‖∇d0‖(n,∞)充分小时,不可压向列型液晶流方程的柯西问题存在整体温和解. 为此, 先作出一系列的估计, 然后利用压缩不动点定理得到该方程的整体温和解的存在性.
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关键词:
- 柯西问题
Abstract: In recent paper, the global solutions to incompressible nematic liquid crystal flow in high dimensions is considered. The authors establish the global existence of the Cauchy problem of the nematic liquid crystal flow in Rn for any initial data (u0,d0) with small ‖u0‖(n,∞)+‖∇d0‖(n,∞). The method is based on a priori estimates and Fixed Point Theorem.-
Keywords:
- Cauchy problem
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