Mathematical treatment of the homogeneous Boltzmann equation for Maxwellian molecules in the presence of singular kernels

This paper proves the existence ofweak solutions to the the spatially homogeneous
Boltzmann equation for Maxwellian molecules, when the initial data are chosen from the
space of all Borel probability measures on R^3 with finite second moments, and the (angular)
collision kernel satisfies a very weak cutoff condition. For the
equation at issue, the uniqueness of the solution corresponding to a specific initial datum has
been recently established in Fournier and Guérin (J Stat Phys 131:749–781, 2008). Finally,
conservation of momentum and energy is also proved for these weak solutions, without
resorting to any boundedness of the entropy.