液晶流方程在弱Lp空间中的解的存在性

On the Existence of Solutions to the Nematic Liquid Crystal Flow in Weak－Lp Spaces

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\|u_0\|_(n,\infty)+\|\nabla d_0\|_(n,\infty)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.

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 R^n for any initial data (u_0,d_0) with small \|u_0\|_(n,\infty)+\|\nabla d_0\|_(n,\infty). The method is based on a priori estimates and Fixed Point Theorem.