Global existence and scattering of small data smooth solutions to quasilinear wave systems on ${\mathbb{R}}^2\times \mathbb{T}$, 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 ${\mathbb{R}}^2\times \mathbb{T}$, Preprint (2024), arXiv:2405.03242], for the $Q_0$-type quadratic nonlinearities, we have shown the global well-posedness and scattering properties of small data smooth solutions to the quasilinear wave systems on ${\mathbb{R}}^2\times \mathbb{T}$. In this paper, we start to solve the global existence problem for the remaining $Q_{\alpha \beta }$-type nonlinearities. By combining these results, we have established the global well-posedness of small solutions on ${\mathbb{R}}^2\times \mathbb{T}$ for the general 3-D quadratically quasilinear wave systems when the related 2-D null conditions are fulfilled.

arXiv admin note: text overlap with arXiv:2405.03242