Spatially-Homogeneous Boltzmann Hierarchy as Averaged Spatially-Inhomogeneous Stochastic Boltzmann Hierarchy
We introduce the stochastic dynamics in the phase space that corresponds to the Boltzmann equation and hierarchy and is the Boltzmann–Grad limit of the Hamiltonian dynamics of systems of hard spheres. By the method of averaging over the space of positions, we derive from it the stochastic dynamics i...
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| Дата: | 2002 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2002
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4042 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| Резюме: | We introduce the stochastic dynamics in the phase space that corresponds to the Boltzmann equation and hierarchy and is the Boltzmann–Grad limit of the Hamiltonian dynamics of systems of hard spheres. By the method of averaging over the space of positions, we derive from it the stochastic dynamics in the momentum space that corresponds to the space-homogeneous Boltzmann equation and hierarchy. Analogous dynamics in the mean-field approximation was postulated by Kac for the explanation of the phenomenon of propagation of chaos and derivation of the Boltzmann equation. |
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