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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2507.03096 |
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| _version_ | 1866913926357188608 |
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| author | Farah, Luiz Gustavo Hespanha, Maicon |
| author_facet | Farah, Luiz Gustavo Hespanha, Maicon |
| contents | This work is concerned with a coupled system of focusing nonlinear Schrödinger equations involving general power-type nonlinearities in the energy-critical setting for dimensions $3\leq d\leq 5$ in the radial setting. Our aim is to demonstrate the scattering versus blow-up dichotomy in the radial case. To achieve this, we first prove the existence of ground state solutions using the concentration-compactness method combined with variational techniques. We then establish finite-time blow-up through a convexity argument and prove scattering by applying the concentration-compactness and rigidity method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03096 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The focusing energy-critical nonlinear Schrödinger system with power-type growth nonlinearities in the radial case Farah, Luiz Gustavo Hespanha, Maicon Analysis of PDEs 35Q44, 35P25, 35B44 This work is concerned with a coupled system of focusing nonlinear Schrödinger equations involving general power-type nonlinearities in the energy-critical setting for dimensions $3\leq d\leq 5$ in the radial setting. Our aim is to demonstrate the scattering versus blow-up dichotomy in the radial case. To achieve this, we first prove the existence of ground state solutions using the concentration-compactness method combined with variational techniques. We then establish finite-time blow-up through a convexity argument and prove scattering by applying the concentration-compactness and rigidity method. |
| title | The focusing energy-critical nonlinear Schrödinger system with power-type growth nonlinearities in the radial case |
| topic | Analysis of PDEs 35Q44, 35P25, 35B44 |
| url | https://arxiv.org/abs/2507.03096 |