Local well-posedness for a system of quadratic derivative nonlinear Schrödinger equations
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908406222159872 |
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| author | Akase, Kohei |
| author_facet | Akase, Kohei |
| contents | We consider the Cauchy problem for a system of quadratic derivative nonlinear Schrödinger equations introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. Under the condition that the flow map fails to be twice differentiable, Hirayama, Kinoshita, and Okamoto (2022) proved the well-posedness by constructing a modified energy and applying the energy method. In the present paper, we improve the well-posedness result under the above condition by using the short-time Fourier restriction norm method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06681 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local well-posedness for a system of quadratic derivative nonlinear Schrödinger equations Akase, Kohei Analysis of PDEs 35Q55 (Primary) 35B30 (Secondary) We consider the Cauchy problem for a system of quadratic derivative nonlinear Schrödinger equations introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. Under the condition that the flow map fails to be twice differentiable, Hirayama, Kinoshita, and Okamoto (2022) proved the well-posedness by constructing a modified energy and applying the energy method. In the present paper, we improve the well-posedness result under the above condition by using the short-time Fourier restriction norm method. |
| title | Local well-posedness for a system of quadratic derivative nonlinear Schrödinger equations |
| topic | Analysis of PDEs 35Q55 (Primary) 35B30 (Secondary) |
| url | https://arxiv.org/abs/2505.06681 |