On the high–low method for NLS on the hyperbolic space
© 2020 Author(s). In this paper, we first prove that the cubic, defocusing nonlinear Schrödinger equation on the two dimensional hyperbolic space with radial initial data in Hs(H2) is globally well-posed and scatters when s > 3/4. Then, we extend the result to nonlinearities of order p > 3. Th...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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AIP Publishing
2021
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| Online Access: | https://hdl.handle.net/1721.1/135430 |
| _version_ | 1826195863870898176 |
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| author | Staffilani, Gigliola Yu, Xueying |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Staffilani, Gigliola Yu, Xueying |
| author_sort | Staffilani, Gigliola |
| collection | MIT |
| description | © 2020 Author(s). In this paper, we first prove that the cubic, defocusing nonlinear Schrödinger equation on the two dimensional hyperbolic space with radial initial data in Hs(H2) is globally well-posed and scatters when s > 3/4. Then, we extend the result to nonlinearities of order p > 3. The result is proved by extending the high-low method of Bourgain in the hyperbolic setting and by using a Morawetz type estimate proved by Staffilani and Ionescu. |
| first_indexed | 2024-09-23T10:16:45Z |
| format | Article |
| id | mit-1721.1/135430 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:16:45Z |
| publishDate | 2021 |
| publisher | AIP Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1354302023-12-22T20:10:35Z On the high–low method for NLS on the hyperbolic space Staffilani, Gigliola Yu, Xueying Massachusetts Institute of Technology. Department of Mathematics © 2020 Author(s). In this paper, we first prove that the cubic, defocusing nonlinear Schrödinger equation on the two dimensional hyperbolic space with radial initial data in Hs(H2) is globally well-posed and scatters when s > 3/4. Then, we extend the result to nonlinearities of order p > 3. The result is proved by extending the high-low method of Bourgain in the hyperbolic setting and by using a Morawetz type estimate proved by Staffilani and Ionescu. 2021-10-27T20:23:26Z 2021-10-27T20:23:26Z 2020 2021-06-01T15:32:39Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/135430 en 10.1063/5.0012061 Journal of Mathematical Physics Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf AIP Publishing arXiv |
| spellingShingle | Staffilani, Gigliola Yu, Xueying On the high–low method for NLS on the hyperbolic space |
| title | On the high–low method for NLS on the hyperbolic space |
| title_full | On the high–low method for NLS on the hyperbolic space |
| title_fullStr | On the high–low method for NLS on the hyperbolic space |
| title_full_unstemmed | On the high–low method for NLS on the hyperbolic space |
| title_short | On the high–low method for NLS on the hyperbolic space |
| title_sort | on the high low method for nls on the hyperbolic space |
| url | https://hdl.handle.net/1721.1/135430 |
| work_keys_str_mv | AT staffilanigigliola onthehighlowmethodfornlsonthehyperbolicspace AT yuxueying onthehighlowmethodfornlsonthehyperbolicspace |