Geodesic
On a rigorous definition of microscopic solutions of the Boltzmann--Enskog equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2013), pp. 270-278

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N. N. Bogolyubov discovered microscopic solutions of the Boltzmann–Enskog equation in kinetic theory of hard spheres. These solutions have the form of sums of the delta-functions and correspond to the exact microscopic dynamics. However, this was done at the “physical level” of rigour. In particular, Bogolyubov did not discuss the products of generalized functions in the collision integral. Here we give a rigorous sense to microscopic solutions by use of regularization. Also, starting from the Vlasov equaton, we obtain new kinetic equations for a hard sphere gas.
Keywords: kinetic equations, Boltzmann–Enskog equation, microscopic solutions, generalized functions.
Mots-clés : Vlasov equation 
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A. S. Trushechkin. On a rigorous definition of microscopic solutions of the Boltzmann--Enskog equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2013), pp. 270-278. http://geodesic.mathdoc.fr/item/VSGTU_2013_1_a26/