A simple one-dimensional model for the three-dimensional vorticity equation. (English) Zbl 0615.76029

Constantin, P.; Lax, P. D.; Majda, A.

Commun. Pure Appl. Math. 38, 715-724 (1985).

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

Keywords:

breakdown of solutions; scale invariance; Hilbert transform; one- dimensional model; three-dimensional vorticity equation; incompressible fluid flow; vorticity equations; three-dimensional Euler equations

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