Miao, ShuangPei, LongYu, Pin2020-01-092020-01-092020-01-092019-10-0110.1093/imrn/rnx086https://infoscience.epfl.ch/handle/20.500.14299/164454WOS:000504073800001This article studies the Cauchy problem for systems of semi-linear wave equations on R3+1 with nonlinear terms satisfying the null conditions. We construct future global-in-time classical solutions with arbitrarily large initial energy. The choice of the large Cauchy initial data is inspired by Christodoulou's characteristic initial data in his work [2] on formation of black holes. The main innovation of the current work is that we discovered a relaxed energy ansatz which allows us to prove decay-in-time-estimate. Therefore, the new estimates can also be applied in studying the Cauchy problem for Einstein equations.Mathematicstext::journal::journal article::research article