The problem of smooth solutions to the Navier Stokes equation

The Navier-Stokes equations describe how fluids (liquids and gases) move. For an incompressible fluid with velocity u and pressure p.

The problem requires mathematicians to prove or disprove that for a given initial velocity field in 3D space, smooth and physically realistic solutions exist for all future time.

Solving the Navier-Stoke equations for fluid flow does not yield precise results on when turbulent flow occurs. Experimental scientists can only make approximate predictions using Reynolds numbers.

In his book "The Universe is a unified object", Author Ngo Quang Ha has analyzed chaotic systems in great detail and demonstrated that the nature of fluid flow is not a chaotic system. From this, the author has proven that smooth solutions to the Navier-Stokes equations always exist.

The book (in English) is available on Amazon: https://www.amazon.com/dp/B0HCGYPFK1