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A simple one-dimensional model for the three-dimensional vorticity equation. (English) Zbl 0615.76029
A simple qualitative one-dimensional model for the, three-dimensional vorticity equation of incompressible fluid flow is developed. This simple model is solved exactly; despite its simplicity, this equation retains several of the most important structural features in the vorticity equations and its solutions exhibit some of the phenomena observed in numerical computations for breakdown for the three-dimensional Euler equations.

MSC:
76B47 Vortex flows for incompressible inviscid fluids
35Q30 Navier-Stokes equations
35B40 Asymptotic behavior of solutions to PDEs
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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