# Uniqueness of Bounded Solutions for the Homogeneous Relativistic Landau Equation with Coulomb Interactions

## TL;DR

This paper proves the uniqueness of weak solutions to the homogeneous relativistic Landau equation with Coulomb interactions under specific integrability conditions, advancing the mathematical understanding of relativistic kinetic equations.

## Contribution

It establishes the first uniqueness result for weak solutions of the relativistic Landau equation with Coulomb interactions under a conditional integrability assumption.

## Key findings

- Uniqueness of weak solutions under certain conditions
- Conditional assumption involving integrability of solutions
- Advancement in mathematical theory of relativistic kinetic equations

## Abstract

We prove the uniqueness of weak solutions to the spatially homogeneous special relativistic Landau equation under the conditional assumption that the solution satisfies $(p^0)^7 F(t,p) \in L^1 ([0,T]; L^\infty)$. The existence of standard weak solutions to the relativistic Landau equation has been shown recently in (arXiv:1806.08720)