Pointwise convergence of Boltzmann solutions for grazing collisions in a Maxwell gas via a probabilitistic interpretation

Hélène Guérin

ESAIM: Probability and Statistics (2010)

  • Volume: 8, page 36-55
  • ISSN: 1292-8100

Abstract

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Using probabilistic tools, this work states a pointwise convergence of function solutions of the 2-dimensional Boltzmann equation to the function solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of Fournier (2000) on the Malliavin calculus for the Boltzmann equation. Moreover, using the particle system introduced by Guérin and Méléard (2003), some simulations of the solution of the Landau equation will be given. This result is original and has not been obtained for the moment by analytical methods.

How to cite

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Guérin, Hélène. "Pointwise convergence of Boltzmann solutions for grazing collisions in a Maxwell gas via a probabilitistic interpretation." ESAIM: Probability and Statistics 8 (2010): 36-55. <http://eudml.org/doc/104321>.

@article{Guérin2010,
abstract = {
Using probabilistic tools, this work states a pointwise convergence of function solutions of the 2-dimensional Boltzmann equation to the function solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of Fournier (2000) on the Malliavin calculus for the Boltzmann equation. Moreover, using the particle system introduced by Guérin and Méléard (2003), some simulations of the solution of the Landau equation will be given. This result is original and has not been obtained for the moment by analytical methods. },
author = {Guérin, Hélène},
journal = {ESAIM: Probability and Statistics},
keywords = {Boltzmann equation without cutoff for a Maxwell gas; Landau equation for a Maxwell gas; nonlinear stochastic differential equations; Malliavin calculus.; Landau equation for a Maxwell gas; Malliavin calculus},
language = {eng},
month = {3},
pages = {36-55},
publisher = {EDP Sciences},
title = {Pointwise convergence of Boltzmann solutions for grazing collisions in a Maxwell gas via a probabilitistic interpretation},
url = {http://eudml.org/doc/104321},
volume = {8},
year = {2010},
}

TY - JOUR
AU - Guérin, Hélène
TI - Pointwise convergence of Boltzmann solutions for grazing collisions in a Maxwell gas via a probabilitistic interpretation
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 8
SP - 36
EP - 55
AB - 
Using probabilistic tools, this work states a pointwise convergence of function solutions of the 2-dimensional Boltzmann equation to the function solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of Fournier (2000) on the Malliavin calculus for the Boltzmann equation. Moreover, using the particle system introduced by Guérin and Méléard (2003), some simulations of the solution of the Landau equation will be given. This result is original and has not been obtained for the moment by analytical methods.
LA - eng
KW - Boltzmann equation without cutoff for a Maxwell gas; Landau equation for a Maxwell gas; nonlinear stochastic differential equations; Malliavin calculus.; Landau equation for a Maxwell gas; Malliavin calculus
UR - http://eudml.org/doc/104321
ER -

References

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