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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2409.05267 |
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| _version_ | 1866909308760883200 |
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| author | Kadar, Istvan |
| author_facet | Kadar, Istvan |
| contents | We study the energy-critical wave equation in three dimensions, focusing on its ground state soliton, denoted by $W$. Using the Poincaré symmetry inherent in the equation, boosting $W$ along any timelike geodesic yields another solution. The slow decay behavior of $W$, $W\sim r^{-1}$, indicates a strong interaction among potential multi-soliton solutions.
In this paper, for arbitrary $N\geq0$, we provide an algorithmic procedure to construct approximate solutions to the energy critical wave equation that: (1) converge to a superposition of solitons, (2) have no outgoing radiation, (3) their error to solve the equation decays like $(t-r)^{-N}$. Then, we show that this approximate solution can be corrected to a real solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05267 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Construction of multi-soliton solutions for the energy critical wave equation in dimension 3 Kadar, Istvan Analysis of PDEs We study the energy-critical wave equation in three dimensions, focusing on its ground state soliton, denoted by $W$. Using the Poincaré symmetry inherent in the equation, boosting $W$ along any timelike geodesic yields another solution. The slow decay behavior of $W$, $W\sim r^{-1}$, indicates a strong interaction among potential multi-soliton solutions. In this paper, for arbitrary $N\geq0$, we provide an algorithmic procedure to construct approximate solutions to the energy critical wave equation that: (1) converge to a superposition of solitons, (2) have no outgoing radiation, (3) their error to solve the equation decays like $(t-r)^{-N}$. Then, we show that this approximate solution can be corrected to a real solution. |
| title | Construction of multi-soliton solutions for the energy critical wave equation in dimension 3 |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.05267 |