NLS with mass-subcritical combined nonlinearities: small mass $L^2$-scattering
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866917064991571968 |
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| author | Bellazzini, Jacopo Forcella, Luigi Georgiev, Vladimir |
| author_facet | Bellazzini, Jacopo Forcella, Luigi Georgiev, Vladimir |
| contents | We prove small data scattering in the mass-subcritical regime for the NLS equation with double nonlinearities, where a focusing leading term is perturbed by a lower order defocusing nonlinear term. Our proof relies on the pseudo-conformal transformation in conjunction with a general variational argument used to obtain the positivity of certain modified energies. Moreover, the smallness assumption is only on the mass of the initial data, and not on the whole $Σ$-norm. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_04340 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | NLS with mass-subcritical combined nonlinearities: small mass $L^2$-scattering Bellazzini, Jacopo Forcella, Luigi Georgiev, Vladimir Analysis of PDEs We prove small data scattering in the mass-subcritical regime for the NLS equation with double nonlinearities, where a focusing leading term is perturbed by a lower order defocusing nonlinear term. Our proof relies on the pseudo-conformal transformation in conjunction with a general variational argument used to obtain the positivity of certain modified energies. Moreover, the smallness assumption is only on the mass of the initial data, and not on the whole $Σ$-norm. |
| title | NLS with mass-subcritical combined nonlinearities: small mass $L^2$-scattering |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.04340 |