Scattering theory For Quadratic Nonlinear Schr\'odinger System in dimension six
| Autor: | Gao, Chuanwei, Meng, Fanfei, Xu, Chengbin, Zheng, Jiqiang |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we study the solutions to the energy-critical quadratic nonlinear Schr\"odinger system in ${\dot H}^1\times{\dot H}^1$, where the sign of its potential energy can not be determined directly. If the initial data ${\rm u}_0$ is radial or non-radial but satisfies the mass-resonance condition, and its energy is below that of the ground state, using the compactness/rigidity method, we give a complete classification of scattering versus blowing-up dichotomies depending on whether the kinetic energy of ${\rm u}_0$ is below or above that of the ground state. Comment: 34 pages |
| Databáze: | arXiv |
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