Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb potential

TL;DR

This paper establishes the uniqueness and local well-posedness of bounded solutions for the homogeneous Landau equation with Coulomb potential, confirming stability relative to initial conditions.

Contribution

It provides the first proof of uniqueness and local well-posedness for bounded solutions in this setting, extending prior existence results.

Findings

Uniqueness of bounded solutions proven

Local well-posedness established

Stability with respect to initial data verified

Abstract

We prove the uniqueness of bounded solutions for the spatially homogeneous Fokker-Planck-Landau equation with a Coulomb potential. Since the local (in time) existence of such solutions has been proved by Arsen'ev-Peskov (1977), we deduce a local well-posedness result. The stability with respect to the initial condition is also checked.