On uniqueness and stability for the Boltzmann-Enskog equation

Authors

Martin Friesen, Dublin City Univ, Sch Math Sci, Glasnevin Campus, Dublin, IrelandFollow
Barbara Ruediger, Univ Wuppertal, Fac Math & Nat Sci, Gaussstr 20, D-42119 Wuppertal, GermanyFollow
Padmanabhan Subdar, Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USAFollow

Document Type

Article

Publication Date

5-2022

Abstract

The time-evolution of a moderately dense gas in a vacuum is described in classical mechanics by a particle density function obtained from the Boltzmann-Enskog equation. Based on a McKean-Vlasov equation with jumps, the associated stochastic process was recently constructed by modified Picard iterations with the mean-field interactions, and more generally, by a system of interacting particles. By the introduction of a shifted distance that exactly compensates for the free transport term that accrues in the spatially inhomogeneous setting, we prove in this work an inequality on the Wasserstein distance for any two measure-valued solutions to the Boltzmann-Enskog equation. As a particular consequence, we find sufficient conditions for the uniqueness and continuous-dependence on initial data for solutions to the Boltzmann-Enskog equation applicable to hard and soft potentials without angular cut-off.

Publication Source (Journal or Book title)

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS

Recommended Citation

Friesen, M., Ruediger, B., & Subdar, P. (2022). On uniqueness and stability for the Boltzmann-Enskog equation. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 29 (3) https://doi.org/10.1007/s00030-022-00755-6