A canonical Hamiltonian formulation of the Navier–Stokes problem

The post presents a Hamiltonian formulation for the Navier-Stokes problem. It demonstrates that while the Navier-Stokes equations cannot be derived from a classical action principle, a second-order formulation can be used to obtain a Hamiltonian structure. The post also discusses the auxiliary conditions and the connection between the conjugate momenta and linear momentum in the Hamiltonian formulation.