Wasserstein Hamiltonian flows
Dynamical Systems
2019-12-17 v2 Analysis of PDEs
Abstract
We establish kinetic Hamiltonian flows in density space embedded with the -Wasserstein metric tensor. We derive the Euler-Lagrange equation in density space, which introduces the associated Hamiltonian flows. We demonstrate that many classical equations, such as Vlasov equation, Schr{\"o}dinger equation and Schr{\"o}dinger bridge problem, can be rewritten as the formalism of Hamiltonian flows in density space.
Keywords
Cite
@article{arxiv.1903.01088,
title = {Wasserstein Hamiltonian flows},
author = {Shui-Nee Chow and Wuchen Li and Haomin Zhou},
journal= {arXiv preprint arXiv:1903.01088},
year = {2019}
}