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Navier-Stokes equations are the most general equations in fluid dynamics:enter image description here

We ususlly derive it by the consevation laws and $F=ma$. But how to derive it from the Action principle or equivalently Euler-Lagrange's equation? Can you give me a Lagrangian (density), or an action to get it?

Not duplicated!

Qmechanic
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user353731
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  • You edited this question to say "Not duplicated!", but, well, just you claiming that doesn't make it true. Can you explain how this question is supposed to be different from the linked duplicate? Both questions ask for an action principle for the Navier-Stokes equations. – ACuriousMind Aug 20 '23 at 13:59
  • @ACuriousMind I think you have wanted to refer to this Q&A, and indirectly you have: https://physics.stackexchange.com/questions/14652/fluid-mechanics-from-a-variational-principle – hyportnex Aug 20 '23 at 14:35
  • @user353731, you may want to look at https://link.aps.org/accepted/10.1103/PhysRevLett.110.174301 and https://arxiv.org/pdf/1412.3082.pdf. The first one discusses the basic ideas of non-conservative systems and the latter applies to to viscous fluids and many other examples. – Amey Joshi Aug 20 '23 at 17:02

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