Geometric hydrodynamics via Madelung transform
Artikel i vetenskaplig tidskrift, 2018

We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important partial differential equations of hydrodynamical origin can be described in this framework in a natural way. In particular, the Madelung transform between the Schrödinger equation and Newton's equations is a symplectomorphism of the corresponding phase spaces. Furthermore, the Madelung transform turns out to be a Kähler map when the space of densities is equipped with the Fisher-Rao information metric. We describe several dynamical applications of these results.

Newton's equations

Hydrodynamics

Quantum information

Fisher-Rao

Infinite-dimensional geometry

Författare

Boris Khesin

University of Toronto

Gerard Misiolek

University of Notre Dame

Klas Modin

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Proceedings of the National Academy of Sciences of the United States of America

0027-8424 (ISSN) 1091-6490 (eISSN)

Vol. 115 6165-6170

Numeriska metoder för beräkningsanatomi

Stiftelsen för Strategisk forskning (SSF), 2013-11-01 -- 2016-10-31.

Geometry and Computational Anatomy (GEOCA)

Europeiska kommissionen (Horisont 2020), 2015-03-01 -- 2017-06-30.

STINT, 2015-04-01 -- 2018-06-30.

Ämneskategorier

Beräkningsmatematik

Geometri

Matematisk analys

DOI

10.1073/pnas.1719346115