Ballistic annihilation in a one-dimensional fluid

A kinetic equation for the two-particle conditional distribution of nearest neighbors is derived as a rigorous consequence of the dynamics of ballistic annihilation. The equation describes completely the evolution of the system when at the initial moment higher order conditional distributions factorize into products of two-particle ones. The derived equation provides a rigorous analytic method to study the process of ballistic annihilation. To illustrate the method the two-velocity case is solved explicitly. It is shown that the annihilation dynamics in one dimension creates strong correlations between the velocities of colliding particles, which rules out the Boltzmann approximation.