The Cauchy Problem for the Vlasov–Poisson System with an External Magnetic Field

We consider the Vlasov–Poisson system with an external homogeneous magnetic field describing the kinetics of a two-component rarefied plasma in the three-dimensional case. For all initial density distribution functions with compact supports, we obtain sufficient conditions on the external magnetic field that provide the global existence of density distribution functions whose supports have arbitrarily small growth with respect to the space variables.