A new approach to velocity averaging lemmas in Besov spaces

Diogo Arsénio, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

We develop a new approach to velocity averaging lemmas based on the dispersive properties of the kinetic transport operator. This method yields unprecedented sharp results in critical Besov spaces, which display, in some cases, a gain of one full derivative. Moreover, the study of dispersion allows to treat the case of LxrLvp integrability with r ≤ p. We also establish results on the control of concentrations in the degenerate Lx,v1 case, which is fundamental in the study of hydrodynamic limits of the Boltzmann equation.

Original languageEnglish (US)
Pages (from-to)495-551
Number of pages57
JournalJournal des Mathematiques Pures et Appliquees
Volume101
Issue number4
DOIs
StatePublished - 2014

Fingerprint

Averaging Lemmas
Boltzmann equation
Besov Spaces
Hydrodynamics
Derivatives
Hydrodynamic Limit
Kinetics
Boltzmann Equation
Integrability
Derivative
Operator

Keywords

  • Besov spaces
  • Dispersion
  • Kinetic transport equation
  • Velocity averaging

ASJC Scopus subject areas

  • Applied Mathematics
  • Mathematics(all)

Cite this

A new approach to velocity averaging lemmas in Besov spaces. / Arsénio, Diogo; Masmoudi, Nader.

In: Journal des Mathematiques Pures et Appliquees, Vol. 101, No. 4, 2014, p. 495-551.

Research output: Contribution to journalArticle

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