Hydrodynamics of probabilistic ballistic annihilation

TL;DR

This paper derives hydrodynamic equations and transport coefficients for a dilute gas of hard spheres that can annihilate or scatter upon collision, revealing stability conditions for the system.

Contribution

It provides the first derivation of hydrodynamic equations and transport coefficients for probabilistic ballistic annihilation systems.

Findings

Hydrodynamic equations are established from the Boltzmann equation.

Transport coefficients are calculated up to Navier-Stokes order.

Stability conditions for the hydrodynamic fields are identified.

Abstract

We consider a dilute gas of hard spheres in dimension $d \geq 2$ that upon collision either annihilate with probability $p$ or undergo an elastic scattering with probability $1-p$. For such a system neither mass, momentum, nor kinetic energy are conserved quantities. We establish the hydrodynamic equations from the Boltzmann equation description. Within the Chapman-Enskog scheme, we determine the transport coefficients up to Navier-Stokes order, and give the closed set of equations for the hydrodynamic fields chosen for the above coarse grained description (density, momentum and kinetic temperature). Linear stability analysis is performed, and the conditions of stability for the local fields are discussed.