Scattering and Blow-Up in Both Time Directions Above the Ground State for the Focusing Nonlinear Schrödinger Equation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917863732805632 |
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| author | Miller, Ian |
| author_facet | Miller, Ian |
| contents | In this article we obtain new scattering and blow-up solutions for intercritical focusing nonlinear Schrödinger equations (NLS) above the ground state mass-energy threshold. The main focus of this article is the establishment of some solutions with arbitrarily large mass-energy which scatter in both time directions. In particular, large mass-energy which does not arise from the Galilean transformation. We additionally obtain new criteria for blow-up in both time directions, as well as improved sufficient conditions for scattering and blow-up in one time direction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06962 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Scattering and Blow-Up in Both Time Directions Above the Ground State for the Focusing Nonlinear Schrödinger Equation Miller, Ian Analysis of PDEs 35A01, 35B44, 35Q55, 35Q60 In this article we obtain new scattering and blow-up solutions for intercritical focusing nonlinear Schrödinger equations (NLS) above the ground state mass-energy threshold. The main focus of this article is the establishment of some solutions with arbitrarily large mass-energy which scatter in both time directions. In particular, large mass-energy which does not arise from the Galilean transformation. We additionally obtain new criteria for blow-up in both time directions, as well as improved sufficient conditions for scattering and blow-up in one time direction. |
| title | Scattering and Blow-Up in Both Time Directions Above the Ground State for the Focusing Nonlinear Schrödinger Equation |
| topic | Analysis of PDEs 35A01, 35B44, 35Q55, 35Q60 |
| url | https://arxiv.org/abs/2412.06962 |