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

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.

arXiv comment32 pages

References in corpus (4)

• Entropy dissipation estimates for the Landau equation in the Coulomb case and applications
• Convolution inequalities for the Boltzmann collision operator
• A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit
• On Strong Convergence to Equilibrium for the Boltzmann Equation with Soft Potentials

Cited by in corpus (1)

• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate