Semilinear damped wave equations with data from Sobolev spaces of negative order: the critical case in Euclidean setting and in the Heisenberg space
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914919414235136 |
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| author | D'Abbicco, Marcello |
| author_facet | D'Abbicco, Marcello |
| contents | In this note, we prove the global existence of solutions to the semilinear damped wave equation in $\mathbb{R}^n$, $n\leq6$, with critical nonlinearity under the assumption that the initial data are small in the energy space $H^1\times L^2$ and under the vanishing condition that the initial data belong to $\dot H^{-γ}$ for some $γ\in(0,n/2)$. A similar result also applies to the damped wave equation in the Heisenberg group $\mathbb{H}^n$, with $n=1,2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11756 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semilinear damped wave equations with data from Sobolev spaces of negative order: the critical case in Euclidean setting and in the Heisenberg space D'Abbicco, Marcello Analysis of PDEs 35L71, 35L15, 35B33, 35A01 In this note, we prove the global existence of solutions to the semilinear damped wave equation in $\mathbb{R}^n$, $n\leq6$, with critical nonlinearity under the assumption that the initial data are small in the energy space $H^1\times L^2$ and under the vanishing condition that the initial data belong to $\dot H^{-γ}$ for some $γ\in(0,n/2)$. A similar result also applies to the damped wave equation in the Heisenberg group $\mathbb{H}^n$, with $n=1,2$. |
| title | Semilinear damped wave equations with data from Sobolev spaces of negative order: the critical case in Euclidean setting and in the Heisenberg space |
| topic | Analysis of PDEs 35L71, 35L15, 35B33, 35A01 |
| url | https://arxiv.org/abs/2408.11756 |