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

ESAIM: Probability and Statistics (2010)

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

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topGuérin, 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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