{
  "id": "1808.09867",
  "version": "v1",
  "published": "2018-08-29T15:01:55.000Z",
  "updated": "2018-08-29T15:01:55.000Z",
  "title": "Quasilinear rough partial differential equations with transport noise",
  "authors": [
    "Antoine Hocquet"
  ],
  "categories": [
    "math.PR",
    "math.AP"
  ],
  "abstract": "We investigate the Cauchy problem for a quasilinear equation of the form $\\mathrm d u=\\mathrm{div}(A(t,x,u)\\nabla u)\\mathrm d t +\\sigma (t,x)\\nabla u\\mathrm d X,$ $u_0\\in L^2$ on the torus $\\mathbb T^d$, where $X$ is a two-step geometric rough path. Using an energy approach, we provide sufficient conditions guaranteeing existence and uniqueness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-29T15:01:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "35A15",
      "35K59"
    ],
    "keywords": [
      "quasilinear rough partial differential equations",
      "transport noise",
      "two-step geometric rough path",
      "sufficient conditions guaranteeing existence",
      "cauchy problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}