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In fluid dynamics I have come across two sets of equations, the Navier-Stokes equation and the Lorenz equations. From what I have read the Navier-Stokes equations always holds. So why do we need the Lorenz equations also? and when would we use them over the Navier-Stokes equations?

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  • $\begingroup$ What the Lorenz equations are used for is described in the wiki article you link. And the reason one might use them over the Navier-Stokes equation is that it's much simpler to solve and study (just like we use Newton's second law even though we know the Schroedinger equation). $\endgroup$ – lemon Aug 11 '16 at 10:10
  • $\begingroup$ What is the similarity between the physical phenomena that Navier-Stokes equation describes and what Lorentz equation describes? $\endgroup$ – Deep Aug 12 '16 at 8:04
  • $\begingroup$ @lemon he didn't link those, a moderator added the links to the question. Click on "edited Aug 11 at 8:51" to see the history. $\endgroup$ – Suzu Hirose Oct 14 '16 at 8:43
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The Navier-Stokes equations are a pretty good description of fluid dynamics, whereas the Lorenz equations are a toy model for the atmosphere.

Like with any toy model, you use the Lorenz equations when you want to model some basic aspect of a real system that you believe is already conveyed by the simplified model. It won't give you realistic results, but might be enough to give you valuable insight into the problem.

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