2nd Law vs Clay Millennium Problem on Navier-Stokes Equations

The Clay Institute Millennium Problem on Navier-Stokes equations is introduced as follows:

• This is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding.
• Waves follow our boat as we meander across the lake, and turbulent air currents follow our flight in a modern jet. Mathematicians and physicists believe that an explanation for and the prediction of both the breeze and the turbulence can be found through an understanding of solutions to the Navier-Stokes equations. 
• Although these equations were written down in the 19th Century, our understanding of them remains minimal. The challenge is to make substantial progress toward a mathematical theory which will unlock the secrets hidden in the Navier-Stokes equations.

The problem is still open. No solution is even in sight after 24 years. No progress at all.

Another main open problem of mathematical physics is the 2nd Law of Thermodynamics, which in particular applies to the flow of fluids such as water and air as governed by Navier-Stokes equations. 

It is thus possible to view the Clay Navier-Stokes Problem as an instance of the 2nd Law of Thermodynamics, and so be reformulated into:

• Mathematical proof of the 2nd Law of Thermodynamics for fluids.       (P)

This version has a more obvious significance and it is possible that a solution can be found and so increase understanding in the spirit of Clay.

A resolution to (P) is presented in recent posts on the 2nd Law.   

I have sent the following letter to the President of the Clay Institute and will report reaction:

Dear President 

No progress towards a solution to the Clay Millennium Problem on Navier-Stokes equations has been 

made over a period of 24 years. A reformulation into a problem which possibly can be solved may better 

meet the stated Clay objective of increasing understanding. 

Thus I suggest a reformulation into a mathematical proof of the 2nd Law of Thermodynamics for fluids as 

expressed here:

https://claesjohnson.blogspot.com/2024/03/2nd-law-vs-clay-millennium-problem-on.html

Sincerely

Claes Johnson

prof em applied mathematics Royal Institute of Technology Stockholm