navier-stokes

Any subsequent theories must converge to Navier-Stokes at the regimes where Navier-Stokes is highly successful.

Summary: Navier-Stokes cannot translate to Boltzmann, because Navier-Stokes is incomplete...

I don't know any continuous model that describes the movement of sand similar to Navier-Stokes for liquid.

Also, the Navier-Stokes equation is typically solved with extremely simple boundary conditions, but reality has surface tension and whatnot.

Solutions to the Navier-Stokes equation are turbulent on all scales, but reality is only turbulent down to the atomic scale.

The lack of solution to the Navier-Stokes equations might prevent you from finding an optimal one.

So, maybe they did well enough with the Navier-Stokes equations, Planck black body radiation, sun spots, etc.

Nonetheless, there was reason for optimism: The leading terms of the series looked like the Navier-Stokes equations when a gas becomes denser and more fluidlike.

The Navier-Stokes equations are the second order expansion of this procedure.

These simulations typically use real wave-front physics (Navier-Stokes), even if simplified.

Ergo: the Navier-Stokes equation is an incomplete description of reality.

Therefore calling the Navier-Stokes equations incomplete is a bit imprecise.

We see the same kind of "well, if we ignore this difficult-to-model process, then the equations look good" in physics, so where's the outcry over the Navier-Stokes theorems?

This is fairly boring because the "incompleteness" is built in to the Navier-Stokes equation from the off, and we (physicists) have been well-aware of it for over a century.