Global Existence in the Critical Space for the Space-Time Monopole Equations

We prove the global existence of solutions in the critical space $$L^1({\mathbb {R}})$$ for space-time monopole equations under the Lorenz gauge condition. The existence of a global solution was showed in our previous paper. Here we adapt a different function space to allow for a simplified proof. We first prove the local existence in $$L^1({\mathbb {R}})$$ and extend the local solution to the global one.