A proof of the smoothing properties of the positive part of Boltzmann's kernel.

@article{Bouchut1998,
abstract = {We give two direct proofs of Sobolev estimates for the positive part of Boltzmann's kernel. The first deals with a cross section with separated variables; no derivative is needed in this case. The second is concerned with a general cross section having one derivative in the angular variable.},
author = {Bouchut, François, Desvillettes, Laurent},
journal = {Revista Matemática Iberoamericana},
keywords = {Colisiones moleculares; Mecánica estadística; Ecuación de Boltzmann; Cinética; Mecánica de fluidos; Gases; integral operator; nonlinear operator; Sobolev space; Boltzmann quadratic kernel; rarefied monoatomic gas; nonlinear Boltzmann equation},
language = {eng},
number = {1},
pages = {47-61},
title = {A proof of the smoothing properties of the positive part of Boltzmann's kernel.},
url = {http://eudml.org/doc/39550},
volume = {14},
year = {1998},
}

TY - JOUR
AU - Bouchut, François
AU - Desvillettes, Laurent
TI - A proof of the smoothing properties of the positive part of Boltzmann's kernel.
JO - Revista Matemática Iberoamericana
PY - 1998
VL - 14
IS - 1
SP - 47
EP - 61
AB - We give two direct proofs of Sobolev estimates for the positive part of Boltzmann's kernel. The first deals with a cross section with separated variables; no derivative is needed in this case. The second is concerned with a general cross section having one derivative in the angular variable.
LA - eng
KW - Colisiones moleculares; Mecánica estadística; Ecuación de Boltzmann; Cinética; Mecánica de fluidos; Gases; integral operator; nonlinear operator; Sobolev space; Boltzmann quadratic kernel; rarefied monoatomic gas; nonlinear Boltzmann equation
UR - http://eudml.org/doc/39550
ER -