Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations in almost critical spaces
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866912021334720512 |
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| author | Hirayama, Hiroyuki Kinoshita, Shinya Okamoto, Mamoru |
| author_facet | Hirayama, Hiroyuki Kinoshita, Shinya Okamoto, Mamoru |
| contents | In this paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrödinger equations introduced by Colin and Colin (2004). We determine an almost optimal Sobolev regularity where the smooth flow map of the Cauchy problem exists, expect for the scaling critical case. This result covers a gap left open in papers of the first and second authors (2014, 2019). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_13072 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations in almost critical spaces Hirayama, Hiroyuki Kinoshita, Shinya Okamoto, Mamoru Analysis of PDEs In this paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schrödinger equations introduced by Colin and Colin (2004). We determine an almost optimal Sobolev regularity where the smooth flow map of the Cauchy problem exists, expect for the scaling critical case. This result covers a gap left open in papers of the first and second authors (2014, 2019). |
| title | Well-posedness for a system of quadratic derivative nonlinear Schrödinger equations in almost critical spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2009.13072 |