On the Measure Valued Solution to the Inelastic Boltzmann Equation with Soft Potentials

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Original languageEnglish
Article number27
Journal / PublicationJournal of Statistical Physics
Issue number2
Online published4 May 2021
Publication statusPublished - May 2021


The goal of this paper is to extend the existence result of measure-valued solution to the Boltzmann equation in elastic interaction, given by Morimoto–Wang–Yang in (J Stat Phys 165:866–906, 2016), to the inelastic Boltzmann equation with moderately soft potentials, which is also an extensive work of our preceding result in the inelastic Maxwellian molecules case. We first prove the existence and uniqueness of measure-valued solution under Grad’s angular cutoff assumption, based on which, we further obtain the existence of non-cutoff solution, for both finite and infinite energy initial datum, by a delicate compactness argument. In addition, the moments propagation and energy dissipation properties are justified for the obtained measure-valued solution as well.

Research Area(s)

  • Boltzmann equation, Measure valued solution, Fourier transform, Non-cutoff assumption, Soft potentials, Inelastic, Probability measure