Smoothing effect of the homogeneous Boltzmann equation with measure valued initial datum

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)429-442
Journal / PublicationAnnales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis
Issue number2
Online published28 Jan 2014
Publication statusPublished - Mar 2015


We justify the smoothing effect for measure valued solutions to the space homogeneous Boltzmann equation of Maxwellian type cross sections. This is the first rigorous proof of the smoothing effect for any measure valued initial data except the single Dirac mass, which gives the optimal description on the regularity of solutions for positive time, caused by the singularity in the cross section. The main new ingredient in the proof is the introduction of a time degenerate coercivity estimate by using the microlocal analysis.

Research Area(s)

  • Boltzmann equation, Coercivity estimate, Measure initial datum, Smoothing effect

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