Global smooth solutions to 2D semilinear wave equations with large data

Abstract: 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.