Global Existence for the Vlasov–Poisson–Landau System in the Critical Besov Space

The dynamics of the electrons interacting with its self‐consistent electrostatic field as well as its grazing collisions with a fixed background of ions can be described by Vlasov–Poisson–Landau (VPL) system. In this paper, we focus on the Cauchy problem for the inhomogeneous VPL system with hard potentials in the whole space . In a perturbation framework, the unique global solution is established in the spatially Besov space. Our proof mainly depends on some trilinear estimates of the nonlinear collision term through the Littlewood–Paley theory and the relationship between homogeneous and nonhomogeneous Chemin–Lerner spaces, which lead to the global energy estimates.