DISSIPATION AND SEMIGROUP ON Hkn : NON-CUTOFF LINEARIZED BOLTZMANN OPERATOR WITH SOFT POTENTIAL

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)3093-3113
Journal / PublicationSIAM Journal on Mathematical Analysis
Volume52
Issue number3
Online published30 Jun 2020
Publication statusPublished - 2020

Abstract

In this paper, we find that the linearized collision operator L of the non-cutoff Boltzmann equation with soft potential generates a strongly continuous semigroup on Hkn, with k, R. In the theory of the Boltzmann equation without angular cutoff, the weighted Sobolev space plays a fundamental role. The proof is based on pseudodifferential calculus, and, in general, for a specific class of Weyl quantization, the L2 dissipation implies Hkn dissipation. This kind of estimate is also known as Gårding's inequality.

Research Area(s)

  • Boltzmann equation, linearized collision operator, pseudodifferential operator, dissipation, strongly continuous semigroup