# Derive Navier-Stokes Equations with Lagrangian and Hamiltonian Mechanics, is that possible?

Hari Seldon
Is that possible to derive the Navier-Stokes equations with Lagrangian and Hamiltonian methods? If yes, how? and if it is not possible, why?

## Answers and Replies

Science Advisor
Gold Member
Did you try Googling this question first? It seems to turn up several hits.

Hari Seldon
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.
Did you try Googling this question first? It seems to turn up several hits.

Science Advisor
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

Hari Seldon, Orodruin and vanhees71
sysprog
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