Local existence of polynomial decay solutions to the Boltzmann equation for soft potentials

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)663-683
Journal / PublicationAnalysis and Applications
Issue number6
Online published11 Dec 2013
Publication statusPublished - Nov 2015


The existence of classical solutions to the Cauchy problem for the Boltzmann equation without angular cutoff has been extensively studied in the framework when the solution has Maxwellian decay in the velocity variable, cf. [6, 8] and the references therein. In this paper, we prove local existence of solutions with polynomial decay in the velocity variable for the Boltzmann equation with soft potential. In the proof, the singular change of variables between post- and pre-collision velocities plays an important role, as well as the regular one introduced in the celebrated cancelation lemma by Alexandre-Desvillettes-Villani-Wennberg [Entropy dissipation and long-range interactions, Arch. Ration. Mech. Anal. 152 (2000) 327-355].

Research Area(s)

  • Boltzmann equation, local existence, non-cutoff soft potential