{
  "id": "2505.06681",
  "version": "v1",
  "published": "2025-05-10T16:10:31.000Z",
  "updated": "2025-05-10T16:10:31.000Z",
  "title": "Local well-posedness for a system of quadratic derivative nonlinear Schrödinger equations",
  "authors": [
    "Kohei Akase"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Cauchy problem for a system of quadratic derivative nonlinear Schr\\\"odinger 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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-10T16:10:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35B30"
    ],
    "keywords": [
      "quadratic derivative nonlinear schrödinger equations",
      "local well-posedness",
      "short-time fourier restriction norm method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}