Hydrodynamics of probabilistic ballistic annihilation

We consider a dilute gas of hard spheres in dimension dgreater than or equal to2 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 is a conserved quantity. 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.