Decay and regularity estimates for the relativistic Landau equation

In 1936 Landau introduced a modification of the Boltzmann equation – the Landau equation – which models a dilute hot plasma in which particles undergo Coulomb interactions. When particle velocities are close to the speed of light, which happens frequently in hot plasmas, effects of Einstein’s theory of special relativity become important. These effects are captured by the relativistic Landau equation, which was introduced by Budker and Beliaev in 1956. 

In this talk we will discuss recent results for the spatially inhomogeneous relativistic Landau equation in the far-from-equilibrium regime, including regularity and decay estimates. Some of the challenges in the analysis of the relativistic Landau equation come from the complex structure of the collision operator and the lack of scaling symmetries enjoyed by the classical counterpart. We will discuss tools and strategies that helped us overcome difficulties caused by the relativistic setting.

The talk is based on joint works with Henderson, Snelson and Tarfulea, and with Strain.