A Priori Estimate of Solutions of a Mixed Problem for the Vlasov–Poisson System with a Homogeneous External Magnetic Field

Abstract We consider the first mixed problem for the Vlasov–Poisson system with a homogeneous external magnetic field in an infinite cylinder. For solutions with supports of the distribution density functions of charged particles lying strictly in the inner cylinder, an a priori estimate of the strength of the self-consistent electric field via the initial distribution density functions is obtained.