Well-posedness of inhomogeneous nonlinear wave equations in $\mathbb{R}^3$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917383965245440 |
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| author | Jiawei, Jiang Boyu Shen Kexue, Li |
| author_facet | Jiawei, Jiang Boyu Shen Kexue, Li |
| contents | This paper is devoted to the well-posedness of the inhomogeneous nonlinear wave equations. By combining Strichartz estimates with the contraction mapping principle, we establish local and global well-posedness in the function spaces $\dot{H}^1(\mathbb{R}^3)\times L^2(\mathbb{R}^3)$ and $\dot{H}^{s+1}(\mathbb{R}^3)\times \dot{H}^{s}(\mathbb{R}^3)$. The analysis is carried out in the energy-subcritical regime. As a consequence, our results extend and improve upon previous results in the literature for general nonlinear wave equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_03703 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Well-posedness of inhomogeneous nonlinear wave equations in $\mathbb{R}^3$ Jiawei, Jiang Boyu Shen Kexue, Li Analysis of PDEs This paper is devoted to the well-posedness of the inhomogeneous nonlinear wave equations. By combining Strichartz estimates with the contraction mapping principle, we establish local and global well-posedness in the function spaces $\dot{H}^1(\mathbb{R}^3)\times L^2(\mathbb{R}^3)$ and $\dot{H}^{s+1}(\mathbb{R}^3)\times \dot{H}^{s}(\mathbb{R}^3)$. The analysis is carried out in the energy-subcritical regime. As a consequence, our results extend and improve upon previous results in the literature for general nonlinear wave equations. |
| title | Well-posedness of inhomogeneous nonlinear wave equations in $\mathbb{R}^3$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.03703 |