2024-04-07 Hacker News Top Articles and Its Summaries
1. A canonical Hamiltonian formulation of the Navier–Stokes problem Total comment counts : 9 Summary The article presents a Hamiltonian formulation of the isotropic Navier-Stokes problem using a minimum-action principle derived from the principle of least squares. The formulation involves varying the velocities and pressure as field quantities, constructing a conserved Hamiltonian functional, and formulating the Hamilton-Jacobi equation. The method can be applied to non-Hamiltonian problems as well. While there is no action integral that yields the Navier-Stokes equations in their usual form, a Hamiltonian formulation can still be found by considering a mathematically equivalent higher-order problem....