Navier-Stokes equations are very difficult differential equations to solve. However, we can use physical reasoning to prove that smooth solutions to the equations always exist
In his book "The Universe Is a Unified Object," author Ngo Quang Ha demonstrated that a fluid system is not a chaotic system sensitive to initial conditions.
This eliminates micro-level uncertainties affecting the fluid system.
Furthermore, based on an analysis of the precise effects of the supply source and the constant fluid flow theorem, the author has demonstrated that a smooth solution to the Navier-Stokes equation always exists.
The book (in English) is available on Amazon: https://www.amazon.com/dp/B0HCGYPFK1