Non-cutoff Boltzmann equation with polynomial decay perturbations

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

9 Scopus Citations
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Author(s)

  • Ricardo ALONSO
  • Yoshinori MORIMOTO
  • Weiran SUN
  • Tong YANG

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)189-292
Journal / PublicationRevista Matematica Iberoamericana
Volume37
Issue number1
Online published26 Aug 2020
Publication statusPublished - 15 Jan 2021

Abstract

The Boltzmann equation without the angular cutoff is considered when the initial data is a small perturbation of a global Maxwellian and decays algebraically in the velocity variable. We obtain a well-posedness theory in the perturbative framework for both mild and strong angular singularities. The three main ingredients in the proof are the moment propagation, the spectral gap of the linearized operator, and the regularizing effect of the linearized operator when the initial data is in a Sobolev space with a negative index. A carefully designed pseudo-differential operator plays a central role in capturing the regularizing effect. In addition, some intrinsic symmetry with respect to the collision operator and an intrinsic functional in the coercivity estimate are essentially used in the commutator estimates for the collision operator with velocity weights.

Research Area(s)

  • Coercivity, Commutator estimates, Moment propagation, Regularizing effect, Spectral gap

Bibliographic Note

Full text of this publication does not contain sufficient affiliation information. With consent from the author(s) concerned, the Research Unit(s) information for this record is based on the existing academic department affiliation of the author(s).

Citation Format(s)

Non-cutoff Boltzmann equation with polynomial decay perturbations. / ALONSO, Ricardo; MORIMOTO, Yoshinori; SUN, Weiran et al.

In: Revista Matematica Iberoamericana, Vol. 37, No. 1, 15.01.2021, p. 189-292.

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