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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2004.08788 |
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| _version_ | 1866914838084583424 |
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| author | Hamano, Masaru Ikeda, Masahiro |
| author_facet | Hamano, Masaru Ikeda, Masahiro |
| contents | In this paper, we consider the nonlinear Schrödinger equation with a repulsive inverse power potential. First, we show that some global well-posedness results and "blow-up or grow-up" results below the ground state without the potential. Then, we prove equivalence of the conditions on the initial data below the ground state without potential. We note that recently, we established existence of a radial ground state and characterized it by the virial functional for NLS with a general potential in two or higher space dimensions in [8]. Then, we also prove a global well-posedness result and a "blow-up or grow-up" result below the radial ground state with a repulsive inverse power potential obtained in [8]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_08788 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Equivalence of conditions on initial data below the ground state to NLS with a repulsive inverse power potential Hamano, Masaru Ikeda, Masahiro Analysis of PDEs In this paper, we consider the nonlinear Schrödinger equation with a repulsive inverse power potential. First, we show that some global well-posedness results and "blow-up or grow-up" results below the ground state without the potential. Then, we prove equivalence of the conditions on the initial data below the ground state without potential. We note that recently, we established existence of a radial ground state and characterized it by the virial functional for NLS with a general potential in two or higher space dimensions in [8]. Then, we also prove a global well-posedness result and a "blow-up or grow-up" result below the radial ground state with a repulsive inverse power potential obtained in [8]. |
| title | Equivalence of conditions on initial data below the ground state to NLS with a repulsive inverse power potential |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2004.08788 |