Scattering for non-radial 3D NLS with combined nonlinearities: the interaction Morawetz approach
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914956365004800 |
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| author | Bellazzini, Jacopo Dinh, Van Duong Forcella, Luigi |
| author_facet | Bellazzini, Jacopo Dinh, Van Duong Forcella, Luigi |
| contents | We give a new proof of the scattering below the ground state energy level for a class of nonlinear Schrödinger equations (NLS) with mass-energy intercritical competing nonlinearities. Specifically, the NLS has a focusing leading order nonlinearity with a defocusing perturbation. Our strategy combines interaction Morawetz estimates à la Dodson-Murphy and a new crucial bound for the Pohozaev functional of localized functions, which is essential to overcome the lack of a monotonicity condition. Furthermore, we give the rate of blow-up for symmetric solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_01600 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Scattering for non-radial 3D NLS with combined nonlinearities: the interaction Morawetz approach Bellazzini, Jacopo Dinh, Van Duong Forcella, Luigi Analysis of PDEs We give a new proof of the scattering below the ground state energy level for a class of nonlinear Schrödinger equations (NLS) with mass-energy intercritical competing nonlinearities. Specifically, the NLS has a focusing leading order nonlinearity with a defocusing perturbation. Our strategy combines interaction Morawetz estimates à la Dodson-Murphy and a new crucial bound for the Pohozaev functional of localized functions, which is essential to overcome the lack of a monotonicity condition. Furthermore, we give the rate of blow-up for symmetric solutions. |
| title | Scattering for non-radial 3D NLS with combined nonlinearities: the interaction Morawetz approach |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2209.01600 |