Existence and uniqueness of L^p solutions to the Boltzmann equation with an angle-potential concentrated collision kernel

2016/11/19 by S. A. Akopian, Akopian, S., Irene M. Gamba +1
Mathematics · Engineering · #Gas Dynamics and Kinetic Theory #Numerical methods in inverse problems #Particle Dynamics in Fluid Flows

paper · pdf · doi:10.48550/arxiv.1611.06316

Abstract

We solve the Cauchy problem associated to the space homogeneous Boltzmann equation with an angle-potential singular concentration modeling the collision kernel, proposed in 2013 by Bobylev and Potapenko. The potential under consideration ranges from Coulomb to hard spheres cases. However, the motivation of such a collision kernel is to treat the case of Coulomb potentials, on which this particular form of collision operator is well defined. We also show that the scaled angle-potential singular concentration in a grazing collisions limit makes the Boltzmann operator converge in the sense of distributions to the Landau operator acting on the Boltzmann solutions.

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