Boundary value problem for the three dimensional time periodic Vlasov-Maxwell system

In this work we study the existence of time periodic weak solution for the three dimensional Vlasov-Maxwell system with boundary conditions. The main idea consists of using the mass, momentum and energy conservation laws which allow us to obtain a priori estimates in the case of a star-shaped bounded spatial domain. We start by constructing time periodic smooth solutions for a regularized system. The existence for the Vlasov-Maxwell system follows by weak stability under uniform estimates. These results apply for both classical and relativistic cases and for systems with several species of particles.

2010 Mathematics Subject Classification

Primary 35F30. Secondary 35B10, 35Q60, 76X05, 82D10.

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Published 1 January 2005