A note on the fourth-order Schrodinger equation with spatially growing inhomogeneous source term
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918493270573056 |
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| author | Alqaied, Alaa Mohammed Saanouni, Tarek |
| author_facet | Alqaied, Alaa Mohammed Saanouni, Tarek |
| contents | This paper studies a non-linear biharmonic Schödinger equation with an unbounded inhomogeneous term. The main goal is to develop a local theory but also a global theory for small data, in the energy space. Moreover, we develop a local theory in Sobolev spaces with lower regularity. The challenge is to deal with the inhomogeneous unbounded term, which broke down the space translation invariance. In order to handle the inhomogenous term, we use some Strauss type estimates, which require a spherically symmetric assumption. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_06985 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the fourth-order Schrodinger equation with spatially growing inhomogeneous source term Alqaied, Alaa Mohammed Saanouni, Tarek Analysis of PDEs 35Q55 This paper studies a non-linear biharmonic Schödinger equation with an unbounded inhomogeneous term. The main goal is to develop a local theory but also a global theory for small data, in the energy space. Moreover, we develop a local theory in Sobolev spaces with lower regularity. The challenge is to deal with the inhomogeneous unbounded term, which broke down the space translation invariance. In order to handle the inhomogenous term, we use some Strauss type estimates, which require a spherically symmetric assumption. |
| title | A note on the fourth-order Schrodinger equation with spatially growing inhomogeneous source term |
| topic | Analysis of PDEs 35Q55 |
| url | https://arxiv.org/abs/2511.06985 |