The gravitational Vlasov-Poisson system with infinite mass and velocities in $\mathbb{R}^3$

Carlo Marchioro (International Research Center for Mathematics and Mechanics of Complex Systems, Universit\’adegli Studi dell’Aquila, L’Aquila, Italy)

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

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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