Global existence and scattering of small data smooth solutions to quasilinear wave systems on $\mathbb{R}^2\times\mathbb{T}$, II
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909423280062464 |
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| author | Hou, Fei Tao, Fei Yin, Huicheng |
| author_facet | Hou, Fei Tao, Fei Yin, Huicheng |
| contents | 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 $Q_{αβ}$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07463 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global existence and scattering of small data smooth solutions to quasilinear wave systems on $\mathbb{R}^2\times\mathbb{T}$, II Hou, Fei Tao, Fei Yin, Huicheng Analysis of PDEs 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 $Q_{αβ}$-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. |
| title | Global existence and scattering of small data smooth solutions to quasilinear wave systems on $\mathbb{R}^2\times\mathbb{T}$, II |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2412.07463 |