I was asserting that IF I have good reason to believe that it MUST exist, then it exists even though I haven't exhibited (ie found) it.

You seem to accept that with Navier Stokes. You seem happy to accept that there is a solution that describes the behaviour of (eg) a mountain stream, even though no one can exhibit that solution. A mountain stream run again with the same boundary conditions would behave the same way, obeying the Navier Stokes law. The Navier Stokes equations provides an existence argument for the solution, even though we can't exhibit such a solution.

I will go a step further. I would argue that we knew that a theory of fluid dynamics must exist even if we hadn't actually discovered the Navier Stokes equations yet, and did not know if we ever would. Because if we run fluid systems again, they respond to the same causes in the way. To assert otherwise is to give the objects in physics some indeterminism that smacks of religion (the god of gaps as Dawkins calls it).

That is in effect my position. To summarise it, if effect follows reliably from cause (which includes effects described probabilistically, which most people are happy with accepting would constitute a valid scientific theory, even if you aren't) then there must exist in principle a description of how the effect depends upon the causes. I never sought to say we would actually find it, in fact I explicitly said we might not.