Abstract
The one-dimensional model for the three-dimensional vorticity equation proposed by Constantin, Lax, and Majda 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.
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References
G. K. Batchelor,An Introduction to Fluid Dynamics (Cambridge University Press, 1967), p. 84.
P. Constantin, P. D. Lax, and A. Majda, A simple one-dimensional model for the three-dimensional vorticity equation,Commun. Pure Appl. Math. 38:715–724 (1985).
T. Kato, Nonstationary flows of viscous and ideal fluids inR 3,J. Funct. Anal. 9:296–305 (1972).
A. Majda, Compressible fluid flow and systems of conservation law in several variables, inApplied Mathematical Science, Vol. 53 (Springer-Verlag, 1984), p. 33.
S. Schochet, Explicit solutions of the viscous model vorticity equation,Commun. Pure Appl. Math. 39:531–537 (1986).
J. Serrin, Mathematical principles of classical fluid mechanics, inHandbuch der Physik, Vol. VIII/1 (Springer-Verlag, 1959), p. 152.
H. Swann, The convergence with vanishing viscosity of nonstationary Navier-Stokes flow to ideal flow inR 3 Trans. Am. Math. Soc. 157:373–397 (1971).
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De Gregorio, S. On a one-dimensional model for the three-dimensional vorticity equation. J Stat Phys 59, 1251–1263 (1990). https://doi.org/10.1007/BF01334750
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DOI: https://doi.org/10.1007/BF01334750