Hermite basis diagonalization for the non-cutoff radially symmetric linearized Boltzmann operator

Lerner, Nicolás; Morimoto, Y.; Pravda-Starov, Karel; Xu, Chao-Jiang

doi:10.5802/slsedp.18

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2014

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Cited by 2 publications

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“…In the recent work [23], we investigate the exact phase space structure of the linearized noncutoff Boltzmann operator with Maxwellian molecules acting on radially symmetric functions with respect to the velocity variable. This linearized non-cutoff radially symmetric Boltzmann operator was shown to be exactly an explicit function of the harmonic oscillator…”

Section: Introductionmentioning

confidence: 99%

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

Lerner¹,

Morimoto²,

Pravda-Starov³

et al. 2013

Kinetic &Amp; Related Models

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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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Section: Introductionmentioning

confidence: 99%