2024/10/28 by Ennis, Christian, Rüdiger, Barbara, Sundar, Padmanabhan
#35Q20 #60H20 #60H30 #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2410.21528
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 ℝ3.