On the Measure Valued Solution to the Inelastic Boltzmann Equation with Soft Potentials

The goal of this paper is to extend the existence result measure-valued solution Boltzmann equation in elastic interaction, given by Morimoto–Wang–Yang (J Stat Phys 165:866–906, 2016), inelastic with moderately soft potentials, which also an extensive work our preceding Maxwellian molecules case. We first prove and uniqueness under Grad’s angular cutoff assumption, based on which, we further obtain non-cutoff solution, for both finite infinite energy initial datum, a delicate compactness argument. In addition, moments propagation dissipation properties are justified obtained as well.