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| Main Author: | |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2104.05502 |
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| _version_ | 1866929389743112192 |
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| author | Dietze, Charlotte |
| author_facet | Dietze, Charlotte |
| contents | We consider the long time dynamics of nonlinear Schrödinger equations with an external potential. More precisely, we look at Hartree type equations in three or higher dimensions with small initial data. We prove an optimal decay estimate, which is comparable to the decay of free solutions. Our proof relies on good control on a high Sobolev norm of the solution to estimate the terms in Duhamel's formula. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_05502 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Dispersive Estimates for Nonlinear Schrödinger Equations with External Potentials Dietze, Charlotte Mathematical Physics Analysis of PDEs 35Q55 We consider the long time dynamics of nonlinear Schrödinger equations with an external potential. More precisely, we look at Hartree type equations in three or higher dimensions with small initial data. We prove an optimal decay estimate, which is comparable to the decay of free solutions. Our proof relies on good control on a high Sobolev norm of the solution to estimate the terms in Duhamel's formula. |
| title | Dispersive Estimates for Nonlinear Schrödinger Equations with External Potentials |
| topic | Mathematical Physics Analysis of PDEs 35Q55 |
| url | https://arxiv.org/abs/2104.05502 |