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

Baranger, 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 -