Year: 2025
Type: article
Abstract: The time evolution of a moderately dense gas evolving in vacuum described by the Boltzmann-Enskog equation is studied. The associated stochastic process, the Boltzmann-Enskog process, was constructed in [1] and further studied in [12, 13]. The process is given by the solution of a McKean-Vlasov equation driven by a Poisson random measure with the compensator depending on the distribution of the solution [1, 12]. The existence of a marginal probability density function at each time for the measure-valued solution is established in this article by using a functional-analytic criterion on Besov spaces [8, 11]. 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 $$\mathbb {R}^3$$ R 3 .
Authors: Christian Ennis, Barbara Rüdiger, Padmanabhan Sundar
Institutions: Louisiana State University, University of Wuppertal
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Award: G7004898485
OpenAlex ID: W4412969995