{
  "id": "1808.07821",
  "version": "v1",
  "published": "2018-08-23T16:12:45.000Z",
  "updated": "2018-08-23T16:12:45.000Z",
  "title": "The Burgers' equation with stochastic transport: shock formation, local and global existence of smooth solutions",
  "authors": [
    "Diego Alonso-Orán",
    "Aythami Bethencourt de León",
    "So Takao"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this work, we examine the solution properties of the Burgers' equation with stochastic transport. First, we prove results on the formation of shocks in the stochastic equation and then obtain a stochastic Rankine-Hugoniot condition that the shocks satisfy. Next, we establish the local existence and uniqueness of smooth solutions in the inviscid case and construct a blow-up criterion. Finally, in the viscous case, we prove global existence and uniqueness of smooth solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-23T16:12:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "smooth solutions",
      "stochastic transport",
      "global existence",
      "shock formation",
      "stochastic rankine-hugoniot condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}