Vortex Dynamics and Singularities in the 3-D Euler Equations
The serious study of singularities in the equations of three dimensional hydrodynamics goes back at least to 1934, and a proof still has not been given that solutions of the Navier-Stokes equations remain smooth.1 Far less is known rigorously about solutions to the Euler equations. Although on physical grounds one might expect a singularity here, the numerical evidence is unpersuasive.
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