Profile decomposition and scattering for general nonlinear Schr{ö}dinger equations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910325465415680 |
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| author | Duyckaerts, Thomas van Tin, Phan |
| author_facet | Duyckaerts, Thomas van Tin, Phan |
| contents | We consider a Schr{ö}dinger equation with a nonlinearity which is a general perturbation of a power'' nonlinearity. We construct a profile decomposition adapted to this nonlinearity.We also prove global existence and scattering in a general defocusing setting, assuming thatthe critical Sobolev norm is bounded in the energy-supercritical case. This generalizes severalprevious works on double-power nonlinearities. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_10939 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Profile decomposition and scattering for general nonlinear Schr{ö}dinger equations Duyckaerts, Thomas van Tin, Phan Analysis of PDEs We consider a Schr{ö}dinger equation with a nonlinearity which is a general perturbation of a power'' nonlinearity. We construct a profile decomposition adapted to this nonlinearity.We also prove global existence and scattering in a general defocusing setting, assuming thatthe critical Sobolev norm is bounded in the energy-supercritical case. This generalizes severalprevious works on double-power nonlinearities. |
| title | Profile decomposition and scattering for general nonlinear Schr{ö}dinger equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2401.10939 |