Density-valued solutions for the Boltzmann-Enskog process

Christian Ennis; Barbara Rüdiger; Padmanabhan Sundar

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arXiv · 2410.21528

Density-valued solutions for the Boltzmann-Enskog process

Christian Ennis·Barbara Rüdiger·Padmanabhan Sundar

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Abstract

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, R\"udiger and Sundar (2017) and further studied by Friesen, R\"udiger 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 $\mathbb{R}^3$.

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Christian Ennis, Barbara Rüdiger, Padmanabhan Sundar. 2024-10-28. Density-valued solutions for the Boltzmann-Enskog process. https://arxiv.org/abs/2410.21528

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