论文标题
Navier-Stokes方程的解决方案的存在和平滑度
No Existence and Smoothness of Solution of the Navier-Stokes Equation
论文作者
论文摘要
Navier-Stokes方程可以以泊松方程式编写。对于通道中的层流（平面Poiseuille流），Navier-Stokes方程在域内具有非零源项和非零的解决方案。对于过渡流，速度曲线被扭曲，速度曲线上出现拐点或扭结，在足够高的雷诺数和较大的干扰下出现。在变形的速度轮廓上的拐点或扭结附近，我们始终可以找到一个源项为零的点。在这一点上，由于零源项，泊松方程是奇异的，并且由于奇异性，目前尚无解决方案。可以得出结论，由于奇异性，全球域中的Navier-Stokes方程没有平滑且身体合理的解决方案。
The Navier-Stokes equation can be written in a form of Poisson equation. For laminar flow in a channel (plane Poiseuille flow), the Navier-Stokes equation has a non-zero source term and a non-zero solution within the domain. For transitional flow, the velocity profile is distorted, and an inflection point or kink appears on the velocity profile, at a sufficiently high Reynolds number and large disturbance. In the vicinity of the inflection point or kink on the distorted velocity profile, we can always find a point where the source term is zero. At this point, the Poisson equation is singular, due to the zero source term, and has no solution at this point due to singularity. It is concluded that there exists no smooth and physically reasonable solutions of the Navier-Stokes equation for transitional flow and turbulence in the global domain due to singularity.
