Revista Matemática Iberoamericana

Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials

Céline Baranger and Clément Mouhot

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This paper deals with explicit spectral gap estimates for the linearized Boltzmann operator with hard potentials (and hard spheres). We prove that it can be reduced to the Maxwellian case, for which explicit estimates are already known. Such a method is constructive, does not rely on Weyl's Theorem and thus does not require Grad's splitting. The more physical idea of the proof is to use geometrical properties of the whole collision operator. In a second part, we use the fact that the Landau operator can be expressed as the limit of the Boltzmann operator as collisions become grazing in order to deduce explicit spectral gap estimates for the linearized Landau operator with hard potentials.

Article information

Rev. Mat. Iberoamericana, Volume 21, Number 3 (2005), 819-841.

First available in Project Euclid: 11 January 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76P05: Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]
Secondary: 82B40: Kinetic theory of gases 82C40: Kinetic theory of gases 82D05: Gases

spectral gap linearized Boltzmann operator Landau linearized operator geometrical properties explicit grazing collision limit hard potentials


Baranger, Céline; Mouhot, Clément. Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials. Rev. Mat. Iberoamericana 21 (2005), no. 3, 819--841.

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