Blow-up rate estimates for the solutions of the bosonic Boltzmann-Nordheim equation

Abstract

In this paper, we study the behavior of a class of mild solutions of the homogeneous and isotropic bosonic Boltzmann-Nordheim equation near the blow-up. We obtain some estimates on the blow-up rate of the solutions and prove that, as long as a solution is bounded above by the critical singularity 1x (the equilibrium solutions behave like this power law near the origin), it remains bounded in the uniform norm. In Sec. III of the paper, we prove a local existence result for a class of measure-valued mild solutions, which is of independent interest and which allows us to solve the Boltzmann-Nordheim equation for some classes of unbounded densities.