Growth of Sobolev norms for 2D cubic nonlinear Schrödinger equation with partial harmonic potential
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| Acceso en línea: | |
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| _version_ | 1866911295435964416 |
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| author | Deng, Mingming Su, Xiaoyan Zheng, Jiqiang |
| author_facet | Deng, Mingming Su, Xiaoyan Zheng, Jiqiang |
| contents | In this paper, we study the $2$D cubic nonlinear Schrödinger equation (NLS) with the partial harmonic potential. First, we prove the local well-posedness in Bourgain spaces by establishing a key bilinear estimate associated with the partial harmonic oscillator. Then, we give the polynomial bound of the Sobolev norms for the solutions using the method of the Planchon, Tzvetkov, and Visciglia. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_02995 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Growth of Sobolev norms for 2D cubic nonlinear Schrödinger equation with partial harmonic potential Deng, Mingming Su, Xiaoyan Zheng, Jiqiang Analysis of PDEs 35A01, 35B40, 35Q55 In this paper, we study the $2$D cubic nonlinear Schrödinger equation (NLS) with the partial harmonic potential. First, we prove the local well-posedness in Bourgain spaces by establishing a key bilinear estimate associated with the partial harmonic oscillator. Then, we give the polynomial bound of the Sobolev norms for the solutions using the method of the Planchon, Tzvetkov, and Visciglia. |
| title | Growth of Sobolev norms for 2D cubic nonlinear Schrödinger equation with partial harmonic potential |
| topic | Analysis of PDEs 35A01, 35B40, 35Q55 |
| url | https://arxiv.org/abs/2304.02995 |