The Boltzmann equation for a multi-species inelastic mixture
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917812615774208 |
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| author | Rey, Thomas Tenna, Tommaso |
| author_facet | Rey, Thomas Tenna, Tommaso |
| contents | A granular gas is a collection of macroscopic particles that interact through energy-dissipating collisions, also known as inelastic collisions. This inelasticity is characterized by a collision mechanics in which mass and momentum are conserved and kinetic energy is dissipated. Such a system can be described by a kinetic equation of the Boltzmann type. Nevertheless, due to the macroscopic aspect of the particles, any realistic description of a granular gas should be written as a mixture model composed of M different species, each with its own mass. We propose in this work such a granular multi-species model and analyse it, providing Povzner-type inequalities, and a Cauchy theory in general Orlicz spaces. We also analyse its large time behavior, showing that it exhibits a mixture analogue of the seminal Haff's Law. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_17027 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Boltzmann equation for a multi-species inelastic mixture Rey, Thomas Tenna, Tommaso Analysis of PDEs Mathematical Physics 82B40, 76T25, 76P05 A granular gas is a collection of macroscopic particles that interact through energy-dissipating collisions, also known as inelastic collisions. This inelasticity is characterized by a collision mechanics in which mass and momentum are conserved and kinetic energy is dissipated. Such a system can be described by a kinetic equation of the Boltzmann type. Nevertheless, due to the macroscopic aspect of the particles, any realistic description of a granular gas should be written as a mixture model composed of M different species, each with its own mass. We propose in this work such a granular multi-species model and analyse it, providing Povzner-type inequalities, and a Cauchy theory in general Orlicz spaces. We also analyse its large time behavior, showing that it exhibits a mixture analogue of the seminal Haff's Law. |
| title | The Boltzmann equation for a multi-species inelastic mixture |
| topic | Analysis of PDEs Mathematical Physics 82B40, 76T25, 76P05 |
| url | https://arxiv.org/abs/2410.17027 |