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

Céline Baranger; Clément Mouhot

Revista Matemática Iberoamericana (2005)

- Volume: 21, Issue: 3, page 819-841
- ISSN: 0213-2230

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topBaranger, Céline, and Mouhot, Clément. "Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials.." Revista Matemática Iberoamericana 21.3 (2005): 819-841. <http://eudml.org/doc/41951>.

@article{Baranger2005,

abstract = {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.},

author = {Baranger, Céline, Mouhot, Clément},

journal = {Revista Matemática Iberoamericana},

keywords = {Ecuación de Boltzmann; Operadores diferenciales; Operadores lineales; grazing collision limit},

language = {eng},

number = {3},

pages = {819-841},

title = {Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials.},

url = {http://eudml.org/doc/41951},

volume = {21},

year = {2005},

}

TY - JOUR

AU - Baranger, Céline

AU - Mouhot, Clément

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

JO - Revista Matemática Iberoamericana

PY - 2005

VL - 21

IS - 3

SP - 819

EP - 841

AB - 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.

LA - eng

KW - Ecuación de Boltzmann; Operadores diferenciales; Operadores lineales; grazing collision limit

UR - http://eudml.org/doc/41951

ER -

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