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On a one-dimensional model for the three-dimensional vorticity equation. (English) Zbl 0712.76027
Summary: The one-dimensional model for the three-dimensional vorticity equation proposed by P. Constantin, P. D. Lax, and A. Majda [Commun. Pure Appl. Math. 38, 715-724 (1985; Zbl 0615.76029)] is discussed. Some unsatisfactory points are examined, especially when the viscosity is introduced. A different model is suggested, which, while less solvable than the previous one, can be more strictly connected with the three-dimensional vorticity behavior. The study is of interest for the numerical treatment of the three-dimensional vorticity equation.

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