Geodesic
On the existence of weak local in time solutions in the form of a cumulant expansion for a chain of Bogolyubov's equations of a one-dimensional symmetric particle system
Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), Tome 42 (2011), pp. 82-94 
G. N. Gubal'. On the existence of weak local in time solutions in the form of a cumulant expansion for a chain of Bogolyubov's equations of a one-dimensional symmetric particle system. Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), Tome 42 (2011), pp. 82-94. http://geodesic.mathdoc.fr/item/CMFD_2011_42_a8/
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     author = {G. N. Gubal'},
     title = {On the existence of weak local in time solutions in the form of a~cumulant expansion for a~chain of {Bogolyubov's} equations of a~one-dimensional symmetric particle system},
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We consider a Cauchy problem for a chain of Bogolyubov equations of an infinite one-dimensional symmetric particle system, where the particles interact with each other by a finite-range pair potential with a hard core. We consider it in the space of sequences of bounded measurable functions. Based on the proposed method of a joint interval for estimates of the volume of the interaction domain and on the derived estimate itself we find a representation of a weak local with respect to time solution in the form of a cumulant expansion. We prove that the considered weak local with respect to time solution is an equilibrium solution if the initial data are equilibrium distribution functions.

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