# Global weak solutions to the relativistic BGK equation

## TL;DR

This paper proves the global existence of weak solutions to the relativistic BGK model, a simplified kinetic equation for relativistic particles, using compactness arguments under minimal initial assumptions.

## Contribution

It establishes the first global existence result for weak solutions to the relativistic BGK equation with minimal initial data assumptions.

## Key findings

- Proved global existence of weak solutions.
- Demonstrated strong compactness of key physical quantities.
- Established results under minimal initial conditions.

## Abstract

In this paper the global existence of weak solutions to the relativistic BGK model for the relativistic Boltzmann equation is analyzed. The proof relies on the strong compactness of the density, velocity and temperature under minimal assumptions on the control of some moments of the initial condition together with the initial entropy.