论文标题
线性操作员的Navier-Stokes方程和半群的存在和平滑度
Existence and smoothness of the Navier-Stokes equations and semigroups of linear operators
论文作者
论文摘要
基于Leray对Navier-Stokes方程的表述以及本文中非线性问题的确切线性表示的条件，给出了Navier-Stokes方程确切的操作员解决方案的紧凑型显式表达式。结果表明，Leray方程的引入的线性操作员是单参数收缩半群的生成器。该半群产生了在平稳的初始条件下，在空间$ \ mathbb {r}^3 $中的Navier-Stokes方程相关问题的独特经典解决方案存在。
Based on Leray's formulation of the Navier-Stokes equations and the conditions of the exact linear representation of the nonlinear problem found in this paper, a compact explicit expression for the exact operator solution of the Navier-Stokes equations is given. It is shown that the introduced linear operator for Leray's equations is the generator of one-parameter contraction semigroup. This semigroup yields the existence of a unique and smooth classical solution of the associated Cauchy problem of Navier-Stokes equations in space $\mathbb{R}^3$ under smooth initial conditions.
