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arXiv · 1903.01088

Wasserstein Hamiltonian flows

Shui-Nee Chow·Wuchen Li·Haomin Zhou
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Abstract

We establish kinetic Hamiltonian flows in density space embedded with the $L^2$-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.

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Shui-Nee Chow, Wuchen Li, Haomin Zhou. 2019-03-04. Wasserstein Hamiltonian flows. https://arxiv.org/abs/1903.01088

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