Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with low regularity periodic initial data
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2013
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| _version_ | 1866914860056444928 |
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| author | Hirayama, Hiroyuki |
| author_facet | Hirayama, Hiroyuki |
| contents | We consider the Cauchy problem of a system of quadratic derivative nonlinear Schrödinger equations which was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. For the nonperiodic case, the author proved the small data global well-posedness and the scattering at the scaling critical regularity for $d\geq 2$ when the coefficients of Laplacian satisfy some condition. In the present paper, we prove the well-posedness of the system for the periodic case. In particular, well-posedness is proved at the scaling critical regularity for $d\geq 3$ under some condition for the coefficients of Laplacian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1311_6102 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with low regularity periodic initial data Hirayama, Hiroyuki Analysis of PDEs We consider the Cauchy problem of a system of quadratic derivative nonlinear Schrödinger equations which was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. For the nonperiodic case, the author proved the small data global well-posedness and the scattering at the scaling critical regularity for $d\geq 2$ when the coefficients of Laplacian satisfy some condition. In the present paper, we prove the well-posedness of the system for the periodic case. In particular, well-posedness is proved at the scaling critical regularity for $d\geq 3$ under some condition for the coefficients of Laplacian. |
| title | Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations with low regularity periodic initial data |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1311.6102 |