Geometric hydrodynamics and infinite-dimensional newton’s equations
Journal article, 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, Mathematical Sciences, Applied Mathematics and Statistics

University of Gothenburg

Bulletin of the American Mathematical Society

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

Vol. 58 3 377-442

Subject Categories

Computational Mathematics

Other Mathematics

Mathematical Analysis



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Latest update

7/8/2021 2