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- Title
THE RIGOROUS DERIVATION OF THE LINEAR LANDAU EQUATION FROM A PARTICLE SYSTEM IN A WEAK-COUPLING LIMIT.
- Authors
Catapano, Nicolo'
- Abstract
We consider a system of N particles interacting via a short-range smooth potential, in a weak-coupling regime. This means that the number of particles N goes to infinity and the range of the potential goes to zero in such a way that Nϵ² = α, with diverging in a suitable way. We provide a rigorous derivation of the Linear Landau equation from this particle system. The strategy of the proof consists in showing the asymptotic equivalence between the one-particle marginal and the solution of the linear Boltzmann equation with vanishing mean free path. This point follows [3] and makes use of technicalities developed in [16]. Then, following the ideas of Landau, we prove the asympotic equivalence between the solutions of the Boltzmann and Landau linear equation in the grazing collision limit.
- Subjects
LANDAU theory; PARTICLE interactions; WEAK interactions (Nuclear physics); BOLTZMANN'S equation; LINEAR equations
- Publication
Kinetic & Related Models, 2018, Vol 11, Issue 3, p647
- ISSN
1937-5093
- Publication type
Article
- DOI
10.3934/krm.2018027