Stochastic dynamics and Boltzmann hierarchy. III
Stochastic dynamics corresponding to the Boltzmann hierarchy is constructed. The Liouville-Itô equations are obtained, from which we derive the Boltzmann hierarchy regarded as an abstract evolution equation. We construct the semigroup of evolution operators and prove the existence of solutions of the Boltzmann hierarchy in the space of sequences of integrable and bounded functions. On the basis of these results, we prove the existence of global solutions of the Boltzmann equation and the existence of the Boltzmann-Grad limit for an arbitrary time interval.
English version (Springer): Ukrainian Mathematical Journal 50 (1998), no. 4, pp 626-645.
Citation Example: Petrina D. Ya., Petrina К. D. Stochastic dynamics and Boltzmann hierarchy. III // Ukr. Mat. Zh. - 1998. - 50, № 4. - pp. 552–569.