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

Published online by Cambridge University Press:  15 September 2004

Hélène Guérin
Hélène Guérin*
Affiliation:
Université Paris 10, UFR SEGMI, Modal'X, 200 avenue de la République, 92000 Nanterre, France; hguerin@ccr.jussieu.fr.
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Abstract


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

Keywords

Boltzmann equation without cutoff for a Maxwell gasLandau equation for a Maxwell gasnonlinear stochastic differential equationsMalliavin calculus.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 8 , August 2004 , pp. 36 - 55
Copyright
© EDP Sciences, SMAI, 2004

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