On the existence of periodic solutions to the modified Korteweg-de Vries equation below $H^{1/2}(\mathbb{T})$
| Autor: | Schippa, Robert |
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| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00028-019-00538-0 |
| Popis: | Existence and a priori estimates for real-valued periodic solutions to the modified Korteweg-de Vries equation with initial data in $H^s$ are established for $s>0$. The short-time Fourier restriction norm method is employed to overcome the derivative loss. Further, non-existence of solutions below $L^2$ is proved conditional upon conjectured linear Strichartz estimates. Comment: 45 pages, minor corrections, explanations added |
| Databáze: | arXiv |
| Externí odkaz: |
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