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On the connection between Hamiltonian many-particle systems and the hydrodynamical equations. (English) Zbl 0850.70166

MSC:
70H05Hamilton’s equations
76B47Vortex flows
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References:
[1] Balescu, R.: Equilibrium and Nonequilibrium Statistical Mechanics. Wiley, 1975. · Zbl 0984.82500
[2] Braun, W. & Hepp, K.: The Vlasov dynamics and its fluctuations in the 1/N limit of interacting classical particles. Commun. Math. Phys. 56, 101-113, 1977. · Zbl 1155.81383 · doi:10.1007/BF01611497
[3] Gingold, R. A. & Monaghan, J. J.: Kernel estimates as a basis for general particle methods in hydrodynamics. J. Comput. Phys. 46, 429-453, 1982. · Zbl 0487.76010 · doi:10.1016/0021-9991(82)90025-0
[4] Lachowicz, M. & Pulvirenti, M.: A stochastic system of particles modelling the Euler equations. Arch. Rational Mech. Anal. 109, 81-93, 1990. · Zbl 0682.76002 · doi:10.1007/BF00377981
[5] Majda, A.: Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables. Springer-Verlag, 1984. · Zbl 0537.76001
[6] Oelschläger, K.: A law of large numbers for moderately interacting diffusion processes. Z. Wahrscheinlichkeitstheorie verw. Gebiete 69, 279-322, 1985. · Zbl 0549.60071 · doi:10.1007/BF02450284
[7] Oelschläger, K.: A fluctuation theorem for moderately interacting diffusion processes. Probab. Th. Rel. Fields 74, 591-616, 1987. · Zbl 0592.60064 · doi:10.1007/BF00363518
[8] Oelschläger, K.: On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes. Probab. Th. Rel. Fields 82, 565-586, 1989. · Zbl 0673.60110 · doi:10.1007/BF00341284
[9] Oelschläger, K.: Large systems of interacting particles and the porous medium equation. J. Diff. Eqs. 88, 294-346, 1990. · Zbl 0734.60101 · doi:10.1016/0022-0396(90)90101-T