论文标题
三个维度和四个维度的Navier-Stokes方程的一类精确解决方案
A class of exact solutions of the Navier-Stokes equations in three and four dimensions
论文作者
论文摘要
本文讨论了不可压缩流体流的Navier-Stokes方程式的一些基本，直观的特性。我们在具有任意数量的尺寸的空间中对Navier-Stokes方程进行了改写的解释。然后，给定平滑的螺线管初始速度矢量场，我们将在空间周期性的速度和压力场进行空间周期性解决方案。在这些解决方案中，所有速度成分在所有坐标方向上都非依赖。
A few basic, intuitive, properties of the Navier-Stokes system of equations for incompressible fluid flows are discussed in this paper. We present a rephrased interpretation of the Navier-Stokes equation in a space having an arbitrary number of dimensions. We then derive spatially periodic solutions for the velocity and pressure fields that span an unbounded domain in three and four dimensions, given a smooth solenoidal initial velocity vector field. In these solutions all velocity components depend non-trivially on all coordinate directions.
