Microscopic solutions of kinetic equations and the irreversibility problem

  • A. S. TrushechkinEmail author


As established by N.N. Bogolyubov, the Boltzmann-Enskog kinetic equation admits the so-called microscopic solutions. These solutions are generalized functions (have the form of sums of delta functions); they correspond to the trajectories of a system of a finite number of balls. However, the existence of these solutions has been established at the “physical” level of rigor. In the present paper, these solutions are assigned a rigorous meaning. It is shown that some other kinetic equations (the Enskog and Vlasov-Enskog equations) also have microscopic solutions. In this sense, one can speak of consistency of these solutions with microscopic dynamics. In addition, new kinetic equations for a gas of elastic balls are obtained through the analysis of a special limit case of the Vlasov equation.


Kinetic Equation Boltzmann Equation STEKLOV Institute Delta Function Mild Solution 
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© Pleiades Publishing, Ltd. 2014

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  2. 2.National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)MoscowRussia

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