{
  "id": "2110.05277",
  "version": "v3",
  "published": "2021-10-11T13:49:01.000Z",
  "updated": "2024-01-28T09:00:41.000Z",
  "title": "On the energy-critical quadratic nonlinear Schrödinger system with three waves",
  "authors": [
    "Fanfei Meng",
    "Sheng Wang",
    "Chengbin Xu"
  ],
  "comment": "In this version, we correct some mistakes, add some chapters and change the title",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article, we consider the dynamics of the energy-critical quadratic nonlinear Schr\\\"odinger system $\\[ \\left\\{ \\begin{aligned} & i u^1_t + \\kappa_1 \\Delta u^1 = -\\overline{u^2}u^3, \\\\ & i u^2_t + \\kappa_2 \\Delta u^2 = -\\overline{u^1}u^3, \\\\ & i u^3_t + \\kappa_3 \\Delta u^3 = -u^1u^2, \\\\ \\end{aligned} \\right. \\qquad (t, x) \\in \\R \\times \\R^6 \\] in energy-space $ {\\dot H}^1 \\times {\\dot H}^1\\times{\\dot H}^1 $, where the sign of potential energy can not be determined. We prove the scattering theory with mass-resonance (or with radial initial data) below ground state via concentration compactness method. We discover a family of new physically conserved quantities with mass-resonance which play an important role in the proof of scattering.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2024-01-28T09:00:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "energy-critical quadratic nonlinear schrödinger system",
      "concentration compactness method",
      "radial initial data",
      "mass-resonance",
      "potential energy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}