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On 24/09/2024 03:00, Lawrence D'Oliveiro wrote:On Mon, 23 Sep 2024 10:38:40 -0000 (UTC), Thomas Koenig wrote:>
(Among thers, he left out turbulence, where we have some understanding,
but do not yet understand the Navier-Stokes equations - one of the
Millenium Problems).
I thought the problem with Navier-Stokes is that it assumes
infinitesimally-small particles of fluid, whereas we know that real fluids
are made up of atoms and molecules.
Remember how Max Planck solved the black-body problem? He knew all about
the previous approach of assuming that matter was made up of little
oscillators, and then trying to work out the limiting behaviour as the
size of those oscillators approached zero -- that didn’t work. So his
breakthrough was in assuming that the oscillators did *not* approach zero
in size, but had some minimum nonzero size. Et voilà ... he got a curve
that actually matched the known behaviour of radiating bodies. And laid
one of the foundation stones of quantum theory in the process.
Seems a similar thing could be done with Navier-Stokes ... ?
Without knowing the history of work on Navier-Stokes, I am /reasonably/
confident that mathematicians have thought about this and tried it.
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