Global Well-posedness for the Fourth-order Nonlinear Schrodinger Equation
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912031199723520 |
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| author | Chen, Mingjuan Lu, Yufeng Wang, Yaqing |
| author_facet | Chen, Mingjuan Lu, Yufeng Wang, Yaqing |
| contents | The local and global well-posedness for the one dimensional fourth-order nonlinear Schrödinger equation are established in the modulation space $M^{s}_{2,q}$ for $s\geq \frac12$ and $2\leq q <\infty$. The local result is based on the $U^p-V^p$ spaces and crucial bilinear estimates. The key ingredient to obtain the global well-posedness is that we achieve a-priori estimates of the solution in modulation spaces by utilizing the power series expansion of the perturbation determinant introduced by Killip-Visan-Zhang for completely integrable PDEs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_11002 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global Well-posedness for the Fourth-order Nonlinear Schrodinger Equation Chen, Mingjuan Lu, Yufeng Wang, Yaqing Analysis of PDEs The local and global well-posedness for the one dimensional fourth-order nonlinear Schrödinger equation are established in the modulation space $M^{s}_{2,q}$ for $s\geq \frac12$ and $2\leq q <\infty$. The local result is based on the $U^p-V^p$ spaces and crucial bilinear estimates. The key ingredient to obtain the global well-posedness is that we achieve a-priori estimates of the solution in modulation spaces by utilizing the power series expansion of the perturbation determinant introduced by Killip-Visan-Zhang for completely integrable PDEs. |
| title | Global Well-posedness for the Fourth-order Nonlinear Schrodinger Equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.11002 |