On global classical solutions of the second mixed problem for a system of Vlasov-Poisson equations in a half-space

A system of Vlasov-Poisson equations with an external magnetic field in a half-space with a Neumann boundary condition for the electric field potential and elastic reflection conditions at the boundary is considered. This problem simulates the kinetics of a high-temperature two-component plasma. For arbitrary initial density distribution functions of charged particles, sufficient conditions for an external magnetic field have been obtained, under which there is a global classical solution with compact supports of the density distribution functions of charged particles lying at some distance from the boundary. The work was supported by the Ministry of Science and Higher Education of the Russian Federation (megagrant agreement №075-15-2022-1115).