K"ahler Geometry and the Navier-Stokes Equations

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We study the Navier-Stokes and Euler equations of incompressible hydrodynamics in two and three spatial dimensions and show how the constraint of incompressiblility leads to equations of Monge--Ampère type for the stream function, when the Laplacian of the pressure is known. In two dimensions a Kähler geometry is described, which is associated with the Monge--Ampère problem. This Kähler structure is then generalised to `two-and-a-half dimensional' flows, of which Burgers' vortex is one example. In three dimensions, we show how a generalized Calabi--Yau structure emerges in a special case.
LaTeX Roy.Soc style, 16 pages

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Exactly Solvable and Integrable Systems, Mathematical Physics, Fluid Dynamics

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http://salesiana.dossiersoluciones.com/handle/123456789/81058

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/nlin/0509023
 http://arxiv.org/abs/nlin/0509023

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arXiv