Regular Lenard-Balescu equations in a Periodic Box

The Lenard-Balescu equation is a collisional kinetic model widely used in plasma physics as a Bogoliubov correction to the meanfield Vlasov theory. Unlike the classical Landau and Boltzmann collision operators, the Lenard-Balescu collisional kernel not only accounts for the binary interaction between particles, but also includes the collective meanfield effects. In this paper, we construct global smooth solutions to the regular Lenard-Balescu equation near global Maxwellians in a periodic box, thus extending the previous work by Duerinckx-Winter that treats the spatially homogenous case to the inhomogenous setting.