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Phase space analysis and functional calculus for the linearized Landau and Boltzmann operators

Authors
  • Lerner, Nicolas
  • Morimoto, Yoshinori
  • Pravda-Starov, Karel
  • Xu, Chao-Jiang
Type
Preprint
Publication Date
Nov 29, 2012
Submission Date
May 16, 2012
Identifiers
arXiv ID: 1205.3688
Source
arXiv
License
Yellow
External links

Abstract

In many works, the linearized non-cutoff Boltzmann operator is considered to behave essentially as a fractional Laplacian. In the present work, we prove that the linearized non-cutoff Boltzmann operator with Maxwellian molecules is exactly equal to a fractional power of the linearized Landau operator which is the sum of the harmonic oscillator and the spherical Laplacian. This result allows to display explicit sharp coercive estimates satisfied by the linearized non-cutoff Boltzmann operator for both Maxwellian and non-Maxwellian molecules.

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