Literature cited
E. A. Novikov, “Dynamics and statistics of a system of vortices,” Zh. Eksp. Teor. Fiz.,68, No. 5 (1975).
S. Kida, “Statistics of a system of line vortices,” J. Phys. Soc. Jpn.,39, No. 5 (1975).
Y. B. Pointin and T. S. Lundgren, “Statistical mechanics of two-dimensional vortices in a bounded container,” Phys. Fluids,19, No. 10 (1976).
Y. B. Pointin and T. S. Lundgren, “Statistical mechanics of two-dimensional vortices,” J. Stat. Phys.,17, No. 5 (1977).
A. J. Chorin, “Numerical study of slightly viscous flow,” J. Fluid Mech.,57, No. 4 (1973).
H. Lamb, Hydrodynamics, Dover (1932).
N. N. Bogolyubov, Problems of Dynamical Theory in Statistical Physics, Collected Works, Vol. 2 [in Russian], Naukova Dumka, Kiev (1970).
R. Balescu, Statistical Mechanics of Charged Particles, Krieger (1963).
R. Balescu and A. Senatorski, “A new approach to the theory of fully developed turbulence,” Ann. Phys.58, No. 2 (1970).
P. Resibois and M. DeLeener, “Irreversibility in Heisenberg spin systems I,” Phys. Rev.,152, No. 1 (1966).
G. K. Batchelor, Introduction to Fluid Dynamics, Cambridge Univ. Press (1967).
N. Rostoker and M. N. Rosenbluth, “Test particles in a completely ionized plasma,” Phys. Fluids,3, No. 1 (1960).
R. H. Kraichnan, “Statistical dynamics of two-dimensional flow,” J. Fluid Mech.,67, Part 1 (1975).
I. Prigozhin, Irreversible Statistical Mechanics [in Russian] Mir, Moscow (1964).
P. Resibois, “New approach to irreversible transport phenomena in plasma dynamics,” Phys. Fluids,6, No. 6 (1963).
G. A. Korn and T. M. Korn, Manual of Mathematics, McGraw-Hill (1967).
I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products, Academic Press, New York (1965).
G. Joyce and D. Montgomery, “Negative temperature states for the two-dimensional guiding-center plasma,” J. Plasma Phys.,10, 1 (1973).
V. P. Starr, Physics of Negative Viscosity Phenomena, McGraw-Hill (1968).
R. Balescu, Equilibrium and Non-Equilibrium Statistical Mechanics, Wiley (1975).
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Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 27–38, May–June, 1983.
The author thanks N. N. Yanenko for interest in the work.
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Grigor'ev, Y.N. Evolution equation for the vortex distribution function in the planar case. J Appl Mech Tech Phys 24, 304–314 (1983). https://doi.org/10.1007/BF00909745
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DOI: https://doi.org/10.1007/BF00909745