GLOBAL EXISTENCE OF MAXWELL KLEIN-GORDON THEORY WITH GENERAL COUPLINGS - (NIM : 20216015), MULYANTO
In this paper we prove the global existence of Maxwell Klein-Gordon equation (MKG) with general couplings in 4-dimensional Minkowski space. We start with the Lagrangian of electromagnetic and complex scalar field with addition of general couplings. Then, we get the solution in form of its curvature using spherical means method for nonlinear wave equation. The solution is bounded by the energy using L-? estimates. For the sake of simplicity, we also use the temporal gauge condition. The result show that the solution is not blow up in finite time. For complete proof of global existence, we show that norm (H2 x H1) in form of energy is not also blow up in finite time.