Uniqueness of higher integrable solution to the Landau equation with Coulomb interactions

Abstract

We are concerned with the uniqueness of weak solution to the spatially homogeneous Landau equation with Coulomb interactions under the assumption that the solution is bounded in the space $L^\infty(0,T,L^p(\R^3))$ for some $p>3/2$. The proof uses a weighted Poincar\'e-Sobolev inequality recently introduced in \cite{GG18}.