Well-posedness for a system of quadratic derivative nonlinear Schr\"odinger equations with radial initial data

Hiroyuki Hirayama; Shinya Kinoshita; Mamoru Okamoto

doi:10.1007/s00023-020-00931-3

Well-posedness for a system of quadratic derivative nonlinear Schr\"odinger equations with radial initial data

Analysis of PDEs 2020-07-13 v1

Authors: Hiroyuki Hirayama , Shinya Kinoshita , Mamoru Okamoto

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Abstract

In the present paper, we consider the Cauchy problem of the system of quadratic derivative nonlinear Schr\"odinger equations. This system was introduced by M. Colin and T. Colin (2004). The first and second authors obtained some well-posedness results in the Sobolev space $H^{s}(\mathbb{R}^d)$ . We improve these results for conditional radial initial data by rewriting the system radial form.

Keywords

quadratic derivative nonlinear schrödinger equations cauchy problem radial initial data well-posedness sobolev space

Cite

@article{arxiv.1811.08324,
  title  = {Well-posedness for a system of quadratic derivative nonlinear Schr\"odinger equations with radial initial data},
  author = {Hiroyuki Hirayama and Shinya Kinoshita and Mamoru Okamoto},
  journal= {arXiv preprint arXiv:1811.08324},
  year   = {2020}
}

Comments

28 pages. arXiv admin note: text overlap with arXiv:1802.06563

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