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

François Bouchut; Laurent Desvillettes

Revista Matemática Iberoamericana (1998)

- Volume: 14, Issue: 1, page 47-61
- ISSN: 0213-2230

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topBouchut, 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 -

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