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A Hydrostatic equilibrium and Navier-Stokes equations

  1. Jun 15, 2017 #1


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    Is it possible to derive the condition for hydrostatic equilibrium or the Navier-Stokes equation for a self-gravitating fluid - e.g. for water on a planet with non-homogeneous density - based on a variational principle?

    (the planet itself is assumed to be a fixed hard core not subject to the variation)
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  3. Jun 15, 2017 #2
    My answer is I don't know. But I do know there is work on the Hamiltonian structure of fluids (see link). I also imagine relativists have work on fluids coupled to gravity in a Lagrangian formulation. However, since you want to produce Navier-Stokes which includes viscosity I worry that might prevent the use of a variational principle.
  4. Jun 18, 2017 #3


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    Hm, are there other replies than just that?

    Thanks a lot. I'll check that as soon as possible.

    Not necessarily including viscosity. I would be glad to see any variational principle. So let's discuss with the Euler equations instead.
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