Polynomial growth of Sobolev norms of solutions of the fractional NLS equation on \T^d
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910073827098624 |
|---|---|
| author | Wang, Jiajun |
| author_facet | Wang, Jiajun |
| contents | In this paper, we prove polynomial growth bounds for the Sobolev norms of solutions to the fractional nonlinear Schrödinger equation on the torus \T^d (d \ge 2), following and extending a result of Joseph Thirouin on \T [Thi17]. The key ingredient is the establishment of Strichartz estimates for the fractional Schrödinger equation on \T^d. To this end, we employ uniform estimates for oscillatory integrals to overcome the lack of uniformity that arises in higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24906 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Polynomial growth of Sobolev norms of solutions of the fractional NLS equation on \T^d Wang, Jiajun Analysis of PDEs In this paper, we prove polynomial growth bounds for the Sobolev norms of solutions to the fractional nonlinear Schrödinger equation on the torus \T^d (d \ge 2), following and extending a result of Joseph Thirouin on \T [Thi17]. The key ingredient is the establishment of Strichartz estimates for the fractional Schrödinger equation on \T^d. To this end, we employ uniform estimates for oscillatory integrals to overcome the lack of uniformity that arises in higher dimensions. |
| title | Polynomial growth of Sobolev norms of solutions of the fractional NLS equation on \T^d |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.24906 |