Comment by sobellian
18 hours ago
NS is a question for natural science. Q: can we model these bodies of discrete particles with a continuous approximation? A: if you do, you can get aphysical singularities.
"If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics."
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.
See 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.
"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.
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