{
  "id": "2304.14866",
  "version": "v1",
  "published": "2023-04-28T14:18:14.000Z",
  "updated": "2023-04-28T14:18:14.000Z",
  "title": "On the global well-posedness of stochastic Schrödinger-Korteweg-de Vries system",
  "authors": [
    "Jie Chen",
    "Fan Gu",
    "Boling Guo"
  ],
  "comment": "24 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we study the global well-posedness of the stochastic S-KdV system in $H^1(\\mathbb{R})\\times H^1(\\mathbb{R})$, which are driven by additive noises. It is difficult to show the global well-posedness of a related perturbation system even for smooth datum and stochastic forces. To overcome it, we introduce a new sequence of approximation equations, which is the key of this paper. We establish priori estimates, global well-posedness and convergences of these approximation equations, which help us to get a pathwise priori estimate of the initial system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-28T14:18:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35Q53",
      "35Q55"
    ],
    "keywords": [
      "stochastic schrödinger-korteweg-de vries system",
      "global well-posedness",
      "approximation equations",
      "stochastic s-kdv system",
      "initial system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}