Measure-valued solution to the inelastic Boltzmann equation for hard potentials without angular cutoff

Abstract

We present a concise summary of our latest findings regarding the global existence of the spatially uniform inelastic Boltzmann equation without angular cutoff [1]. Our results establish the global existence of measure-valued solutions for the general hard potential long-range interaction within the collision kernel. The initial condition only requires a constraint in terms of the (2 + κ)-moment for κ > 0, with no entropy assumption needed. To validate our conclusions, it is essential to develop an enhanced Povzner-type inequality.