  The Lenard-Balescu equation was formally derived in the 1960s as the
fundamental description of the collisional process in a spatially homogeneous
system of interacting particles. It can be viewed as correcting the standard
Landau equation by taking into account collective screening effects. Due to the
reputed complexity of the Lenard-Balescu equation in case of Coulomb
interactions, its mathematical theory has remained void apart from the
linearized setting. In this contribution, we focus on the case of smooth
interactions and we show that dynamical screening effects can then be handled
perturbatively. Taking inspiration from the Landau theory, we establish global
well-posedness close to equilibrium, local well-posedness away from
equilibrium, and we discuss the convergence to equilibrium and the validity of
the Landau approximation.
