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 L-p by applying a bilinear estimate. From a priori L-p estimates, we can extend the local solution to the global one. For the critical case L-1, the concentration of the solution is denied to show the time global solvability. (C) 2015 Elsevier Inc. All rights reserved.