Dynamics of 3D focusing, energy-critical wave equation with radial data
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917205941157888 |
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| author | Shen, Ruipeng |
| author_facet | Shen, Ruipeng |
| contents | In this article we discuss the long-time dynamics of the radial solutions to the energy-critical wave equation in 3-dimensional space. Given a solution defined for all time $t\geq 0$, we show that the soliton resolution phenomenon happens at all times $t>0$ except for a few relatively short time intervals. The main tool is the radiation theory of wave equations and the major observation of this work is a correspondence between the energy radiation and the soliton resolution/collision behaviour of solutions. We also give a few applications of the main observation on the type II blow-up solutions and ``one pass'' theory near pure mutli-solitons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00391 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of 3D focusing, energy-critical wave equation with radial data Shen, Ruipeng Analysis of PDEs 35L05, 35L71 In this article we discuss the long-time dynamics of the radial solutions to the energy-critical wave equation in 3-dimensional space. Given a solution defined for all time $t\geq 0$, we show that the soliton resolution phenomenon happens at all times $t>0$ except for a few relatively short time intervals. The main tool is the radiation theory of wave equations and the major observation of this work is a correspondence between the energy radiation and the soliton resolution/collision behaviour of solutions. We also give a few applications of the main observation on the type II blow-up solutions and ``one pass'' theory near pure mutli-solitons. |
| title | Dynamics of 3D focusing, energy-critical wave equation with radial data |
| topic | Analysis of PDEs 35L05, 35L71 |
| url | https://arxiv.org/abs/2507.00391 |