On an evolution system describing self-gravitating particles in microcanonical setting

TL;DR

This paper proves the global existence of solutions for a gravitational particle system with diffusion, including Fermi-Dirac and polytropic cases, in a fixed energy microcanonical setting.

Contribution

It establishes the global in time existence of solutions for a broad class of self-gravitating particle systems with diffusion, extending to Fermi-Dirac and polytropic models.

Findings

Proves global existence of solutions for the system.

Includes models with Fermi-Dirac diffusion.

Applicable to dissipative polytropic cases.

Abstract

The global in time existence of solutions of a system describing the interaction of gravitationally attracting particles with a general diffusion term and fixed energy is proved. The presented theory covers the case of the model with diffusion that obeys Fermi-Dirac statistics. Some of the results apply to the dissipative polytropic case as well.