# The massless electron limit for the Vlasov-Poisson-Landau system

# The massless electron limit for the Vlasov-Poisson-Landau system

**In-Person Talk**

The Vlasov-Poisson-Landau is a kinetic model for ionized plasmas. In this talk, I will describe the massless electron limit for this system. This leads to a simplified model for the positively charged ions, where ion-electron collisions can be ignored. In joint work with Yan Guo, we give a rigorous justification of this limit. A major difficulty is that the limit is singular: specifically, there is a small factor of epsilon in front of the time derivative of the electron distribution. In general, such a coefficient could cause rapid oscillations or growth. However, in this case, the VPL system is degenerate parabolic. With some work, we can use this parabolicity to show that the electrons remain close to the limiting distribution, via precise energy estimates and a form of hypocoervicity.