Global Existence of Maxwell Klein Gordon Theory with General Couplings

Abstract

In this paper, we prove the global existence of Maxwell Klein Gordon equation (MKG) with the addition of general couplings in 4-dimensional Minkowski space. It is well known that the MKG system is globally well-posed in consideration of the Coulomb gauge condition for finite energy, while here we use the temporal gauge condition to prove its existence. The result shows that the solution does not blow up in finite time. For complete proof of global existence, we show that (H2 × H1) norm in the form of “modification of energy” is not also blow up in finite time.