Global weak solutions and uniform Lp-stability of the Boltzmann–Enskog equation

We present the regularity theory of renormalized solutions and uniform Lp-stability estimates of the Boltzmann–Enskog model. We use a multi-dimensional Bony-type functional to control the time–phase space integral of a truncated collision operator. We employ Cercignaniʼs arguments and a Bony-type functional to show that the renormalized solutions to the Boltzmann–Enskog model are weak solutions in usual distributional sense. For the uniform Lp-stability estimate, we use Luʼs trick together with the Hölder inequality.