Global well-posedness for the higher order non-linear Schrödinger equation on modulations spaces
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929608658518016 |
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| author | Carvajal, X. Gamboa, P. Santos, R. |
| author_facet | Carvajal, X. Gamboa, P. Santos, R. |
| contents | We consider the initial value problem (IVP) associated to a higher order nonlinear Schrödinger (h-NLS) equation $ \partial_{t}u+ia \partial^{2}_{x}u+ b\partial^{3}_{x}u+ic_1|u|^{2}u+c_2 |u|^{2}\partial_{x}u=0,
\quad x,t \in \mathbb{R}, $ for given data in the modulation space $M_s^{2,p}(\mathbb{R})$. Using ideias of Killip, Visan, Zhang, Oh, Wang, we prove that the IVP associated to the h-NLS equation is globally well-posed in the modulation spaces $M^{s,p}$ for $s\geq\frac14$ and $p\geq2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_03497 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global well-posedness for the higher order non-linear Schrödinger equation on modulations spaces Carvajal, X. Gamboa, P. Santos, R. Analysis of PDEs We consider the initial value problem (IVP) associated to a higher order nonlinear Schrödinger (h-NLS) equation $ \partial_{t}u+ia \partial^{2}_{x}u+ b\partial^{3}_{x}u+ic_1|u|^{2}u+c_2 |u|^{2}\partial_{x}u=0, \quad x,t \in \mathbb{R}, $ for given data in the modulation space $M_s^{2,p}(\mathbb{R})$. Using ideias of Killip, Visan, Zhang, Oh, Wang, we prove that the IVP associated to the h-NLS equation is globally well-posed in the modulation spaces $M^{s,p}$ for $s\geq\frac14$ and $p\geq2$. |
| title | Global well-posedness for the higher order non-linear Schrödinger equation on modulations spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2310.03497 |