Piecewise and parallelism combined with the Navier stokes equation allows for pieces of fluidity to connect.
The reason its hard to find a smooth equation to fire or gas is because space is open so the fluid dynamics works in pieces as opposed to single smooth equation. there is smoothness in gas but it interacts in pieces thus you have to account for it in the maths.
There should then be such an equation that proves the smoothness in piecewise with parrallelability for a;; fluid dynamics and it should be relatively hard to solve.
In order to solve this problem one needs to search for it.
With graph coloring solved it should now be possible to master with a computer such a complex proof and with the use of careful dynaveo manipulation of Relationship and tie functions a sufficient relationship and tie Equation should be possible and it should be possible to prove this smooth.
Although smooth when you are dealing with gas you are dealing with a smooth system of bodies not a smooth system of a body this I suspect is where all the trouble lyes.