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

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-09-29 DOI:10.1112/jlms.70303

Fei Hou, Fei Tao, Huicheng Yin

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引用次数: 0

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 $R^{2} \times T$ , 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 $R^{2} \times T$ . In this paper, we start to solve the global existence problem for the remaining $Q_{α β}$ -type nonlinearities. By combining these results, we have established the global well-posedness of small solutions on $R^{2} \times T$ for the general 3-D quadratically quasilinear wave systems when the related 2-D null conditions are fulfilled.

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r2 × T $\mathbb {R}^2\乘以\mathbb {T}$上拟线性波系统小数据光滑解的整体存在性和散射性，[j]

在我们之前的论文[侯飞，陶飞，尹慧成，一类拟线性波系统在r2 × T上的小数据光滑解的整体存在性和散射性]，$\mathbb {R}^2\times \mathbb {T}$, Preprint (2024), arXiv:2405.03242]，对于q0 $Q_0$型二次非线性，我们给出了r2 × T上拟线性波系统小数据光滑解的全局适定性和散射性质$\mathbb {R}^2\times \mathbb {T}$。本文开始求解剩余Q α β $Q_{\alpha \beta }$型非线性的全局存在性问题。结合这些结果，我们建立了一般三维二次拟线性波系统在r2 × T $\mathbb {R}^2\times \mathbb {T}$上，当相关的二维零条件满足时，小解的全局适定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.