It is proved that if the Navier-Stokes problem is considered in ℝ³, then the initial velocity has to be zero. This is the paradox. The consequences of this paradox are: a) The NSP is contradictory physically and mathematically; it is not a correct formulation of the problem of motion of the incompressible viscous fluid. b) The solution to the NSP does not exist on [0, ∞). This solves one of the millennium problems.

中文翻译：

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纳维-斯托克斯方程悖论

证明如果在ℝ ^{3 中}考虑Navier-Stokes 问题，则初始速度必须为零。这就是悖论。这个悖论的后果是： a) NSP 在物理和数学上是矛盾的；它不是不可压缩粘性流体运动问题的正确表述。b) NSP 的解在 [0, ∞) 上不存在。这解决了千年难题之一。