Asymptotic of grazing collisions for the spatially homogeneous Boltzmann equation for soft and Coulomb potentials

David Godinho (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

We give an explicit bound for the Wasserstein distance with quadratic cost between the solutions of Boltzmann's and Landau's equations in the case of soft and Coulomb potentials. This gives an explicit rate of convergence for the grazing collisions limit. Our result is local in time for very soft and Coulomb potentials and global in time for moderately soft potentials.

Mots clés: Kinetic Theory; Boltzmann equation; Landau equation; Grazing collisions

Domaines: Probabilités [math.PR]; Physique mathématique [math-ph]

David Godinho. Asymptotic of grazing collisions for the spatially homogeneous Boltzmann equation for soft and Coulomb potentials. 2013. ⟨hal-00793604⟩