Vlasov–Poisson Equation in Besov Space

Abstract

We study the local-in-time well-posedness of Vlasov–Poisson equation in Besov space for the large initial data. To accomplish it, we establish commutator estimates in Besov space which are quite useful in dealing with the electronic term $\nabla_{x} \phi$. Also, the $L^p$-$L^q$ type estimates for the electronic term $\nabla_{x} \phi$ are established, which are not only useful in the estimate for Poisson equation, but also play a fundamentally important role in commutator estimates involving the electronic term $\nabla_{x} \phi$.