ABSTRACT

In this talk we will explain very recent results on the relativistic Landau equation (with no spatial dependence). Despite its physical importance, this equation has not received a lot of mathematical attention we think due to the extreme complexity of the relativistic structure of the kernel of the collision operator. In this talk we first largely decompose the structure of the relativistic Landau collision operator. After that we prove the global Entropy dissipation estimate. Then we prove the propagation of any polynomial moment for a weak solution. Lastly we prove the existence of a true weak solution for a large class of initial data. This is a joint with Maja Taskovic. Our aim is to develop a theory for this understudied and physically important model.