{
  "id": "1808.05967",
  "version": "v1",
  "published": "2018-08-17T18:23:17.000Z",
  "updated": "2018-08-17T18:23:17.000Z",
  "title": "On singularity formation for the two dimensional unsteady Prandtl's system",
  "authors": [
    "Charles Collot",
    "Tej-Eddine Ghoul",
    "Slim Ibrahim",
    "Nader Masmoudi"
  ],
  "comment": "45 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the two dimensional unsteady Prandtl's system. For a special class of outer Euler flows and solutions of the Prandtl system, the trace of the tangential derivative along the transversal axis solves a closed one dimensional equation. We give a precise description of singular solutions for this reduced problem. A stable blow-up pattern and a countable family of other unstable solutions are found. The blow-up point is ejected to infinity in finite time, and the solutions form a plateau with growing length. The proof uses modulation techniques and different energy estimates in the various zones of interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-17T18:23:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B44",
      "35Q35",
      "35K58",
      "35B40"
    ],
    "keywords": [
      "dimensional unsteady prandtls system",
      "singularity formation",
      "outer euler flows",
      "energy estimates",
      "prandtl system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}