Ballistic annihilation with continuous isotropic initial velocity distribution

Ballistic annihilation with continuous initial velocity distributions is in vestigated in the framework of the Boltzmann equation. The particle density and the rms velocity decay as c similar to t(-alpha) and <(<nu>)over bar> similar to t(-beta), with the exponents depending on the initial velocity d istribution and the spatial dimension d. For instance, in one dimension for the uniform initial velocity distribution beta = 0.230472.... In the oppos ite extreme d --> infinity, the dynamics is universal and beta --> (1 - 2(- 1)/(2))d(-1). We also solve the Boltzmann equation for Maxwell particles an d very hard particles in arbitrary spatial dimension. These solvable cases provide bounds for the decay exponents of the hard sphere gas.