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

S. Akopian; I. M. Gamba

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arXiv · 1611.06316

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

S. Akopian·I. M. Gamba

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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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BibTeX RIS

S. Akopian, I. M. Gamba. 2016-11-19. Existence and uniqueness of $L^p$ solutions to the Boltzmann equation with an angle-potential concentrated collision kernel. https://arxiv.org/abs/1611.06316

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