This is a wrong interpretation. Physicists have a shit-ton of models that produce "aphysical singularities", they just work around those to get meaningful answers anyway. This is a whole trope and stereotype. Some of the most successfull and accurate predictions in all of physics come out after you discard a bunch of singularities.
replySee e.g. https://en.wikipedia.org/wiki/Renormalization
Nobody who actually works in fluid dynamics on any sort of application gives a hoot about the N-S millenium problem. Many do not even know what it is. There is no practical effect of this proof on how we do fluid mechanics.
Whether or not ways exist to work around the singularities, that they exist is surely of note. Before von Neumann formalized QM people were still doing QM, okay fine. But it's wrong to then say von Neumann was doing no physics of note.
reply"Does there exist a pathological combination of smooth body forces and initial conditions for this set of PDEs, where singularities appear, which by the way is completely impossible to actually create in the real world unless you are a literal God?" is a question of math, not physics. This is a hill I will die on.
replyAFAICT the unforced problem is still open. I don't think we've established that you need to be a literal God to create a finite-time blowup.
replyIf you think about what it actually means to have a time-varying smooth body force defined in all of 3-space, you fairly quickly come to that kind of conclusion.
replyEven if someone comes up with a construction that does not require any forcing, it is going to be some extremely weird initial conditions that you will never be able to even approximate in reality unless you can move all the individual molecules of a fluid around and set their initial velocities from a far distance.
The unforced problem is still open.
replyYou realize that hill is a mathematical argument, not a physical hill.
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