A scattering theory construction of dynamical solitons in 3d
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866909144499355648 |
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| author | Kadar, Istvan |
| author_facet | Kadar, Istvan |
| contents | We study the energy critical wave equation in 3 dimensions around a single soliton. We obtain energy boundedness (modulo unstable modes) for the linearised problem. We use this to construct scattering solutions in a neighbourhood of timelike infinity ($i_+$), provided the data on null infinity ($\scri$) decay polynomially. Moreover, the solutions we construct are conormal on a blow-up of Minkowski space. The methods of proof also extend to some energy supercritical modifications of the equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_13891 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A scattering theory construction of dynamical solitons in 3d Kadar, Istvan Analysis of PDEs We study the energy critical wave equation in 3 dimensions around a single soliton. We obtain energy boundedness (modulo unstable modes) for the linearised problem. We use this to construct scattering solutions in a neighbourhood of timelike infinity ($i_+$), provided the data on null infinity ($\scri$) decay polynomially. Moreover, the solutions we construct are conormal on a blow-up of Minkowski space. The methods of proof also extend to some energy supercritical modifications of the equation. |
| title | A scattering theory construction of dynamical solitons in 3d |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.13891 |