Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case
Abstract We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions $$D \ge 4$$ D...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer International Publishing
2023
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| Online Access: | https://hdl.handle.net/1721.1/152404 |
| _version_ | 1826189155686678528 |
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| author | Jendrej, Jacek Lawrie, Andrew |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Jendrej, Jacek Lawrie, Andrew |
| author_sort | Jendrej, Jacek |
| collection | MIT |
| description | Abstract
We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions
$$D \ge 4$$
D
≥
4
. This equation has a unique (up to sign and scale) nontrivial, finite energy stationary solution W, called the ground state. We prove that every finite energy solution with bounded energy norm resolves, continuously in time, into a finite superposition of asymptotically decoupled copies of the ground state and free radiation. |
| first_indexed | 2024-09-23T08:10:45Z |
| format | Article |
| id | mit-1721.1/152404 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2025-02-19T04:16:55Z |
| publishDate | 2023 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1524042024-12-23T06:28:56Z Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case Jendrej, Jacek Lawrie, Andrew Massachusetts Institute of Technology. Department of Mathematics Abstract We consider the focusing energy-critical nonlinear wave equation for radially symmetric initial data in space dimensions $$D \ge 4$$ D ≥ 4 . This equation has a unique (up to sign and scale) nontrivial, finite energy stationary solution W, called the ground state. We prove that every finite energy solution with bounded energy norm resolves, continuously in time, into a finite superposition of asymptotically decoupled copies of the ground state and free radiation. 2023-10-10T18:51:11Z 2023-10-10T18:51:11Z 2023-10-06 2023-10-07T03:14:03Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/152404 Annals of PDE. 2023 Oct 06;9(2):18 en https://doi.org/10.1007/s40818-023-00159-4 Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ The Author(s), under exclusive licence to Springer Nature Switzerland AG application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Jendrej, Jacek Lawrie, Andrew Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case |
| title | Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case |
| title_full | Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case |
| title_fullStr | Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case |
| title_full_unstemmed | Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case |
| title_short | Soliton Resolution for the Energy-Critical Nonlinear Wave Equation in the Radial Case |
| title_sort | soliton resolution for the energy critical nonlinear wave equation in the radial case |
| url | https://hdl.handle.net/1721.1/152404 |
| work_keys_str_mv | AT jendrejjacek solitonresolutionfortheenergycriticalnonlinearwaveequationintheradialcase AT lawrieandrew solitonresolutionfortheenergycriticalnonlinearwaveequationintheradialcase |