Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation on cylindrical spaces
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909059599302656 |
|---|---|
| author | Osawa, Satoshi Takaoka, Hideo |
| author_facet | Osawa, Satoshi Takaoka, Hideo |
| contents | We prove that the Zakharov-Kuznetsov equation on cylindrical spaces is globally well-posed below the energy norm. As is known, local well-posedness below energy space was obtained by the first author. We adapt I-method to extend the solutions globally in time. Using modified energies, we obtain the polynomial bounds on the $H^s$ growth for the global solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00453 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation on cylindrical spaces Osawa, Satoshi Takaoka, Hideo Analysis of PDEs 35Q53, 42B37 We prove that the Zakharov-Kuznetsov equation on cylindrical spaces is globally well-posed below the energy norm. As is known, local well-posedness below energy space was obtained by the first author. We adapt I-method to extend the solutions globally in time. Using modified energies, we obtain the polynomial bounds on the $H^s$ growth for the global solutions. |
| title | Global well-posedness for the Cauchy problem of the Zakharov-Kuznetsov equation on cylindrical spaces |
| topic | Analysis of PDEs 35Q53, 42B37 |
| url | https://arxiv.org/abs/2401.00453 |