Density-valued solutions for the Boltzmann-Enskog process
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866912209974591488 |
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| author | Ennis, Christian Rüdiger, Barbara Sundar, Padmanabhan |
| author_facet | Ennis, Christian Rüdiger, Barbara Sundar, Padmanabhan |
| contents | The time evolution of moderately dense gas evolving in vacuum described by the Boltzmann-Enskog equation is studied. The associated stochastic process, the Boltzmann-Enskog process, was constructed by Albeverio, Rüdiger and Sundar (2017) and further studied by Friesen, Rüdiger and Sundar (2019, 2022). The process is given by the solution of a McKean-Vlasov equation driven by a Poisson random measure, the compensator depending on the distribution of the solution. The existence of a marginal probability density function at each time for the measure-valued solution is established here by using a functional-analytic criterion in Besov spaces Debussche and Romito (2014), and Fournier (2015). In addition to existence, the density is shown to reside in a Besov space. The support of the velocity marginal distribution is shown to be the whole of $\mathbb{R}^3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_21528 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Density-valued solutions for the Boltzmann-Enskog process Ennis, Christian Rüdiger, Barbara Sundar, Padmanabhan Probability 35Q20, 60H20, 60H30 The time evolution of moderately dense gas evolving in vacuum described by the Boltzmann-Enskog equation is studied. The associated stochastic process, the Boltzmann-Enskog process, was constructed by Albeverio, Rüdiger and Sundar (2017) and further studied by Friesen, Rüdiger and Sundar (2019, 2022). The process is given by the solution of a McKean-Vlasov equation driven by a Poisson random measure, the compensator depending on the distribution of the solution. The existence of a marginal probability density function at each time for the measure-valued solution is established here by using a functional-analytic criterion in Besov spaces Debussche and Romito (2014), and Fournier (2015). In addition to existence, the density is shown to reside in a Besov space. The support of the velocity marginal distribution is shown to be the whole of $\mathbb{R}^3$. |
| title | Density-valued solutions for the Boltzmann-Enskog process |
| topic | Probability 35Q20, 60H20, 60H30 |
| url | https://arxiv.org/abs/2410.21528 |