nLab hydrodynamics

Idea

Hydrodynamics is the dynamics of liquids, i.e. of low compressible fluids. It is part of rheology, a general science of fluids. For a while this entry will have a redirect fluid dynamics.

Related entries

• Navier-Stokes equation

• Kadomtsev-Petviashvili equation

• magnetohydrodynamics

• phase of matter

• fluid/gravity correspondence

References

• Vladimir Arnold: Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits, Annales de l’Institut Fourier 16 1 (1966) 319–361 [numdam:AIF_1966__16_1_319_0/]

  (application of infinite-dimensional Lie groups)

• L. D. Landau, E. M. Lifschitz, Fluid mechanics (Russian original is Hydrodynamics), vol. 6 of the Course of Theoretical Physics, Pergamon Press

• Vladimir Arnold, Boris Khesin, Topological methods in hydrodynamics, Applied Mathematical Sciences 125, Springer 1998 (doi:10.1007/b97593)

  (using methods of topology and homotopy theory)

• Dennis Sullivan, Algebra, topology and algebraic topology of 3D ideal fluids, arxiv/1010.2721

  (some ideas on need for higher geometry at the end)

• Benjamin Doyon, Lecture notes on Generalised Hydrodynamics (arXiv:1912.08496)

See also

• Wikipedia, Fluid dynamics

• Alexander Migdal: Geometric Solution of Turbulence as Diffusion in Loop Space [arXiv:2511.02165]

A symplecto/Poisson geometrically organized account of ideal relativistic hydrodynamics:

• Nikita Nekrasov, Paul Wiegmann: Fluid dynamics as intersection problem [arXiv:2512.25053]