奇数维可压缩液晶流方程解的逐点估计

首先, 本文利用标准的能量估计方法得到高维(3 维及以上) 的液晶流方程组小初值经典解的整体存在性. 然后, 本文运用Green 函数方法, 得到奇数维情形(3 维及以上) 该解的逐点估计. 该结果表明, 密度ρ和动量m同Navier-Stokes 方程组一样满足一般Huygens 原理, 而单位向量场d则没有这种现象, 其有着与热方程的解类似的时空估计.

Pointwise estimates of solution to compressible nematic liquid crystal flow in odd dimensions

The Cauchy problem of the compressible nematic liquid crystal flow is considered. We obtain the global existence of the classical solution under the smallness assumption on the initial perturbation. Furthermore, by using Green function method, the pointwise estimates of the solution are given, which imply generalized Huygens principle for density ρ and momentum m, while the derivative of the unit-vector field d behaves like the solution of the Heat equation. The phenomenon is different from the Navier-stokes equations.