Global solutions to space–time monopole equations in one space dimension

We prove global existence of solutions to space–time monopole equations in one space dimension. Observing the null structure of the system, we first prove local existence in LpLp by applying a bilinear estimate. From a priori LpLp estimates, we can extend the local solution to the global one. For the critical case L1L1, the concentration of the solution is denied to show the time global solvability.