Global dynamics of a supercritical wave equation in a large data regime
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918503229947904 |
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| author | Dong, Shijie Wyatt, Zoe Zhao, Jingya |
| author_facet | Dong, Shijie Wyatt, Zoe Zhao, Jingya |
| contents | We prove the existence of global solutions to the nonlinear wave equation in $\mathbb{R}^{1+3}$ $$Φ_{tt} - ΔΦ\pm Φ|Φ|^{p-1} = 0$$ in the energy-supercritical regime $p>5$, for a class of large initial data. Our initial data can be decomposed into two pieces, one which is dispersed in the sense of having large $L^2$ norm, while the other piece takes a localised short-pulse form. Consequently, we can obtain global existence for a class of initial data which is large in every homogeneous Sobolev norm $\dot{H}^s_x$ with $s \geq 0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_15662 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Global dynamics of a supercritical wave equation in a large data regime Dong, Shijie Wyatt, Zoe Zhao, Jingya Analysis of PDEs We prove the existence of global solutions to the nonlinear wave equation in $\mathbb{R}^{1+3}$ $$Φ_{tt} - ΔΦ\pm Φ|Φ|^{p-1} = 0$$ in the energy-supercritical regime $p>5$, for a class of large initial data. Our initial data can be decomposed into two pieces, one which is dispersed in the sense of having large $L^2$ norm, while the other piece takes a localised short-pulse form. Consequently, we can obtain global existence for a class of initial data which is large in every homogeneous Sobolev norm $\dot{H}^s_x$ with $s \geq 0$. |
| title | Global dynamics of a supercritical wave equation in a large data regime |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.15662 |