Geometric hydrodynamics and infinite-dimensional newton’s equations
Artikel i vetenskaplig tidskrift, 2021

We revisit the geodesic approach to ideal hydrodynamics and present a related geometric framework for Newton’s equations on groups of diffeomorphisms and spaces of probability densities. The latter setting is sufficiently general to include equations of compressible and incompressible fluid dynamics, magnetohydrodynamics, shallow water systems and equations of relativistic fluids. We illustrate this with a survey of selected examples, as well as with new results, using the tools of infinite-dimensional information geometry, optimal transport, the Madelung transform, and the formalism of symplectic and Poisson reduction.


Boris Khesin

University of Toronto

Gerard Misiołek

University of Notre Dame

Klas Modin

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

Göteborgs universitet

Bulletin of the American Mathematical Society

0273-0979 (ISSN) 1088-9485 (eISSN)

Vol. 58 3 377-442



Annan matematik

Matematisk analys



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