Contents Online
Communications in Mathematical Sciences
Volume 22 (2024)
Number 5
The gravitational Vlasov-Poisson system with infinite mass and velocities in $\mathbb{R}^3$
Pages: 1455 – 1461
(Fast Communication)
DOI: https://dx.doi.org/10.4310/CMS.2024.v22.n5.a11
Authors
Abstract
We study existence and uniqueness of the solution to the gravitational Vlasov–Poisson system evolving in $\mathbb{R}^3$. It is assumed that initially the particles are distributed according to a spatial density with a power-law decay in space, allowing for unbounded mass, and an exponential decay in velocities given by a Maxwell–Boltzmann law. We extend a classical result which holds for systems with finite total mass.
Keywords
Vlasov–Poisson equation, gravitational interaction, infinite mass
2010 Mathematics Subject Classification
35Q83, 35Q85, 85A05
The authors’ work was performed under the auspices of GNFM-INDAM and the Italian Ministry of the University (MUR).
Received 17 January 2024
Accepted 27 January 2024
Published 15 July 2024