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

Bouchut, François, and Desvillettes, Laurent. "A proof of the smoothing properties of the positive part of Boltzmann's kernel.." Revista Matemática Iberoamericana 14.1 (1998): 47-61. <http://eudml.org/doc/39550>.

@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 -