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Kinetic and Related Models (KRM)
 

On the Kac model for the Landau equation

Pages: 333 - 344, Volume 4, Issue 1, March 2011      doi:10.3934/krm.2011.4.333

 
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Evelyne Miot - Laboratoire de Mathématiques, Université Paris-Sud 11, bât. 425, 91405 Orsay, France (email)
Mario Pulvirenti - Dipartimento di Matematica Guido Castelnuovo, Università La Sapienza - Roma, P.le A. Moro, 5 00185 Roma, Italy (email)
Chiara Saffirio - Dipartimento di Matematica Guido Castelnuovo, Università La Sapienza - Roma, P.le A. Moro, 5 00185 Roma, Italy (email)

Abstract: We introduce a $N$-particle system which approximates, in the mean-field limit, the solutions of the Landau equation with Coulomb singularity. This model plays the same role as the Kac's model for the homogeneous Boltzmann equation. We use compactness arguments following [11].

Keywords:  N-particle system, Kac's model for the Landau equation, N-particle hierarchy, propagation of chaos.
Mathematics Subject Classification:  35D30, 35Q20, 35Q70, 35Q82.

Received: October 2010;      Revised: October 2010;      Available Online: January 2011.

 References