From Boltzmann to Landau: Analysis and numerics in plasma applications

We will present a revision to approximations limits from the classical non-linear Boltzmann equation Coulombic interactions in the
grazing collision limit to the Landau equation for a variety of angular cross sections and their approximations rates from its solutions to a solution of the Landau equation. These rates can vary strongly depending of the singularity rate of the angular part of the cross section.

In addition, we will describe deterministic conservative solvers to Vlasov-Poisson Landau that enable estimates towards rigorous stability and convergence, and present numerical simulations.

This work can be found in a series of manuscripts involving collaborations with A. Bobylev, J. Haack, I. Potapenko and C. Zhang.