Uniform boundedness of conformal energy for the 3D nonlinear wave equation
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915550334025728 |
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| author | Zhao, Jingya |
| author_facet | Zhao, Jingya |
| contents | In this paper, we study three-dimensional nonlinear wave equations under the null condition, a fundamental model in the theory of nonlinear wave-type equations, initially investigated by Christodoulou \cite{Christodoulou86} and Klainerman \cite{Klainerman86}. For a class of large initial data, we establish global existence and linear scattering of solutions by combining refined energy estimates with a bootstrap argument. Moreover, we prove that the lower-order conformal energy remains uniformly bounded for all time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_12103 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform boundedness of conformal energy for the 3D nonlinear wave equation Zhao, Jingya Analysis of PDEs In this paper, we study three-dimensional nonlinear wave equations under the null condition, a fundamental model in the theory of nonlinear wave-type equations, initially investigated by Christodoulou \cite{Christodoulou86} and Klainerman \cite{Klainerman86}. For a class of large initial data, we establish global existence and linear scattering of solutions by combining refined energy estimates with a bootstrap argument. Moreover, we prove that the lower-order conformal energy remains uniformly bounded for all time. |
| title | Uniform boundedness of conformal energy for the 3D nonlinear wave equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2501.12103 |