Kinetic interaction Morawetz and concentration estimates

Abstract: In this paper we will develop the kinetic interaction Morawetz estimate for mesoscopic evolutions. Furthermore, we will find a new a-priori bound and introduce the notion of interaction uncertainty. We will demonstrate that interaction uncertainty goes to infinity with time and that the interactions, averaged over time, concentrate within a specific collection of blind cones with an arbitrarily small apex angle. These results are solely based on conservation laws and thereby are all true for the Boltzmann equation and its different variants