2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/81058We 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 pagesExactly Solvable and Integrable SystemsMathematical PhysicsFluid Dynamicstext