Derivation of the Higher Order Boltzmann Equation for Hard Spheres
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929493864611840 |
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| author | Ampatzoglou, Ioakeim Pavlović, Nataša Warner, William |
| author_facet | Ampatzoglou, Ioakeim Pavlović, Nataša Warner, William |
| contents | In this paper we complete the program initiated by the first and second authors and rigorously derive a Boltzmann-type equation that incorporates higher order collisions among gas particles. More precisely, starting from a finite $N$-particle system where the particles can perform symmetric hard sphere type interactions up to arbitrarily high order $M$, we derive a kinetic equation which consists of a linear combination of higher order collisional terms. We identify the new scaling regime that facilitates such collisions and systematically generalize geometric techniques allowing us to analyze the correlation of potentially distinct order recollisions as time evolves. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05669 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Derivation of the Higher Order Boltzmann Equation for Hard Spheres Ampatzoglou, Ioakeim Pavlović, Nataša Warner, William Analysis of PDEs Mathematical Physics In this paper we complete the program initiated by the first and second authors and rigorously derive a Boltzmann-type equation that incorporates higher order collisions among gas particles. More precisely, starting from a finite $N$-particle system where the particles can perform symmetric hard sphere type interactions up to arbitrarily high order $M$, we derive a kinetic equation which consists of a linear combination of higher order collisional terms. We identify the new scaling regime that facilitates such collisions and systematically generalize geometric techniques allowing us to analyze the correlation of potentially distinct order recollisions as time evolves. |
| title | Derivation of the Higher Order Boltzmann Equation for Hard Spheres |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2409.05669 |