A local existence result for a plasma physics model containing a fully coupled magnetic field

A local existence theorem is proved for classical solutions of the Vlasov-Poisswell system, a set of collisionless equations used in plasma physics. Although the method employed is standard, there are several technical difficulties in the treatment of this system that arise mainly from the, compared to related systems, special form of the electric-field term. Furthermore, uniqueness of classical solutions is proved and a continuation criterion for solutions well known for other collisionless kinetic equations is established. Finally, a global existence result for a regularized version of the system is derived and comments are given on the problem of obtaining global weak solutions.