Global existence and scattering of small data smooth solutions to quasilinear wave systems on R2×T$\mathbb {R}^2\times \mathbb {T}$, II

Abstract In our previous paper [Fei Hou, Fei Tao, Huicheng Yin, Global existence and scattering of small data smooth solutions to a class of quasilinear wave systems on , Preprint (2024), arXiv:2405.03242], for the ‐type quadratic nonlinearities, we have shown the global well‐posedness and scattering properties of small data smooth solutions to the quasilinear wave systems on . In this paper, we start to solve the global existence problem for the remaining ‐type nonlinearities. By combining these results, we have established the global well‐posedness of small solutions on for the general 3‐D quadratically quasilinear wave systems when the related 2‐D null conditions are fulfilled.