{
  "id": "2212.14552",
  "version": "v1",
  "published": "2022-12-30T05:05:07.000Z",
  "updated": "2022-12-30T05:05:07.000Z",
  "title": "Averaging principle for slow-fast systems of stochastic PDEs with rough coefficients",
  "authors": [
    "Sandra Cerrai",
    "Yichun Zhu"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we consider a class of slow-fast systems of stochastic partial differential equations where the nonlinearity in the slow equation is not continuous and unbounded. We first provide conditions that ensure the existence of a martingale solution. Then we prove that the laws of the slow motions are tight, and any of their limiting points is a martingale solution for a suitable averaged equation. Our results apply to systems of stochastic reaction-diffusion equations where the reaction term in the slow equation is only continuous and has polynomial growth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-30T05:05:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "slow-fast systems",
      "rough coefficients",
      "stochastic pdes",
      "averaging principle",
      "slow equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}