# The onset of fluid-dynamical behavior in relativistic kinetic theory

## TL;DR

This paper investigates the divergence of the Chapman-Enskog expansion in relativistic kinetic theory, revealing that non-hydrodynamic modes cause the series to have zero radius of convergence in a Bjorken expanding fluid.

## Contribution

It demonstrates the non-convergence of the Knudsen series due to non-hydrodynamic modes in relativistic kinetic theory.

## Key findings

- The Chapman-Enskog series diverges for a Bjorken expanding fluid.
- Non-hydrodynamic modes cause non-perturbative contributions.
- The series has zero radius of convergence.

## Abstract

In this proceedings we discuss recent findings regarding the large order behavior of the Chapman-Enskog expansion in relativistic kinetic theory. It is shown that this series in powers of the Knudsen number has zero radius of convergence in the case of a Bjorken expanding fluid described by the Boltzmann equation in the relaxation time approximation. This divergence stems from the presence of non-hydrodynamic modes, which give non-perturbative contributions to the Knudsen series.