Vlasov-Poisson equations for a two-component plasma in a homogeneous magnetic field

This paper is concerned with the first mixed problem for the Vlasov-Poisson equations in an infinite cylinder, a problem describing the evolution of the density distribution of ions and electrons in a high temperature plasma under an external magnetic field. A stationary solution is constructed for which the charged-particle density distributions are supported in a strictly interior cylinder. A classical solution for which the supports of the charged-particle density distributions are at a distance from the cylindrical boundary is shown to exist and to be unique in some neighbourhood of the stationary solution.