5 ms·
This result applies to turbulent flows. Not all flows are turbulent, and the Navier-Stokes equations should describe laminar, transitional, and turbulent flows
by atrettel 7y ago
This result applies to turbulent flows. Not all flows are turbulent, and the Navier-Stokes equations should describe laminar, transitional, and turbulent flows (3 major regimes of fluid flow). Transitional flows are not yet fully turbulent and can behave differently than a fully turbulent flow behaves. My background is in fluid dynamics, so I can't speak directly about the mathematical difficulties in proving the existence and uniqueness of solutions of the Navier-Stokes equations. However, I can say that any general solution to the Navier-Stokes equations must apply to laminar, transitional, and turbulent flows, so finding a particular result for turbulent flows alone is insufficient. Any such result would have to transcend its regime in some way. Surely I think more proofs like this couldn't hurt, but I do not see any direct connection between this result and the Navier-Stokes existence/uniqueness problem (coming from a fluid dynamics background).
Hacker News has already discussed this result previously in an earlier thread: https://news.ycombinator.com/item?id=21771684 https://news.ycombinator.com/item?id=21771684
- mar77i 7y agoDamn it, you beat me to bringing up laminar flow!