Graduate Deriving Navier-Stokes: Lagrangian & Hamiltonian Methods

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The discussion centers on the possibility of deriving the Navier-Stokes equations using Lagrangian and Hamiltonian methods. Participants express that while there are resources available online, they seek a more structured approach involving generalized coordinates and kinetic energy calculations. It is noted that the Navier-Stokes equations involve energy dissipation, complicating their derivation through these methods. A reference to Peter Constantin's work suggests an Eulerian-Lagrangian approach may be viable. Ultimately, the conversation reflects a desire for clarity on the application of these mathematical frameworks to fluid dynamics.
Hari Seldon
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Is that possible to derive the Navier-Stokes equations with Lagrangian and Hamiltonian methods? If yes, how? and if it is not possible, why?
 
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Did you try Googling this question first? It seems to turn up several hits.
 
Hello, thank you for your reply. Yes, I tried to Google it, but I didn't find what I wanted. I expected an approach like, for example, estabilish the generalized coordinates, calculate the kinetic energy and so on. Finally, that is why I wrote here, I tought that maybe I was thinking in a wrong way.
boneh3ad said:
Did you try Googling this question first? It seems to turn up several hits.
 
Hari Seldon said:
Is that possible to derive the Navier-Stokes equations with Lagrangian and Hamiltonian methods? If yes, how? and if it is not possible, why?
the Navier-Stokes is a system with energy dissipation. The variational principle for the Euler equations is contained in M. Taylor's PDE vol 3
 
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Hari Seldon said:
Is that possible to derive the Navier-Stokes equations with Lagrangian and Hamiltonian methods? If yes, how? and if it is not possible, why?
It seems to some that those equations could be approached with such methods:

An Eulerian-Lagrangian approach to the Navier-Stokes equations. ##-## by Peter Constantin ##-## https://web.math.princeton.edu/~const/xlnsF.pdf
 

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