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by leephillips
1488 days ago
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The NS equations are a good description of approximately Newtonian fluids like water within certain regimes (nonrelativistic velocities, larger than atomic scales, far above 0°K, etc.). “Imagination” was not the best choice of word on my part. I meant that DEs are mathematical objects; their connection to physical systems is made by the scientist, not inherent in themselves. Whether the scientist guessed right is determined by experiment. The first people to suggest that the NS equations were a good description of Newtonian fluids had a model for fluid behavior in their imaginations. We know it was a good model because of experiment. But even if the NS equations described nothing in nature, their solutions, chaotic and otherwise, would have whatever properties they have. Note that there is no Largrangian for the NS equations, by the way. |
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> Note that there is no Lagrangian for the NS equations, by the way.
I don't know much about fluid dynamics, but I was under the impression that Bennett derives the Lagrangian form in the book Lagrangian Fluid Dynamics