  We are interested in coupled semi-linear wave equations satisfying the null
condition in two space dimensions, a basic model in nonlinear wave equations.
Our aim is to establish global existence of smooth solutions to this system
with large initial data of short pulse type. Major difficulties arise due to
the largeness of initial data and the slow decay nature of 2D wave equations.
To overcome the difficulties, by careful examination of the local solutions, we
adapt various vector-field methods to different spacetime regions with several
novel weighted energy estimates.
