Existence of global solutions to the Fokas-Lenells equation with arbitrary spectral singularities
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912789124087808 |
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| author | Li, Yuan Cheng, Qiaoyuan Fan, Engui |
| author_facet | Li, Yuan Cheng, Qiaoyuan Fan, Engui |
| contents | We establish the global existence of solutions to the Fokas-Lenells equation for any initial data in a weighted Sobolev space $H^{3}(\mathbb{R})\cap H^{2,1}(\mathbb{R})$.This result removes all spectral restrictions on the initial data required in our previous work.
The proof primarily relies on the inverse scattering transform formulated as new Riemann-Hilbert problems and Zhou's $L^{2}$-Sobolev bijectivity theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21536 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of global solutions to the Fokas-Lenells equation with arbitrary spectral singularities Li, Yuan Cheng, Qiaoyuan Fan, Engui Analysis of PDEs Mathematical Physics We establish the global existence of solutions to the Fokas-Lenells equation for any initial data in a weighted Sobolev space $H^{3}(\mathbb{R})\cap H^{2,1}(\mathbb{R})$.This result removes all spectral restrictions on the initial data required in our previous work. The proof primarily relies on the inverse scattering transform formulated as new Riemann-Hilbert problems and Zhou's $L^{2}$-Sobolev bijectivity theory. |
| title | Existence of global solutions to the Fokas-Lenells equation with arbitrary spectral singularities |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2512.21536 |