{
  "id": "0910.3136",
  "version": "v1",
  "published": "2009-10-16T15:20:14.000Z",
  "updated": "2009-10-16T15:20:14.000Z",
  "title": "Well-posedness in smooth function spaces for the moving-boundary 1-D compressible Euler equations in physical vacuum",
  "authors": [
    "Daniel Coutand",
    "Steve Shkoller"
  ],
  "comment": "27 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The free-boundary compressible 1-D Euler equations with moving physical vacuum boundary are a system of hyperbolic conservation laws which are both characteristic and degenerate. The physical vacuum singularity (or rate-of-degeneracy) requires the sound speed $c= \\gamma \\rho^{\\gamma -1}$ to scale as the square-root of the distance to the vacuum boundary, and has attracted a great deal of attention in recent years. We establish the existence of unique solutions to this system on a short time-interval, which are smooth (in Sobolev spaces) all the way to the moving boundary. The proof is founded on a new higher-order Hardy-type inequality in conjunction with an approximation of the Euler equations consisting of a particular degenerate parabolic regularization. Our regular solutions can be viewed as degenerate viscosity solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-10-16T15:20:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L65",
      "35L70",
      "35L80",
      "35Q35",
      "35R35",
      "76B03"
    ],
    "keywords": [
      "smooth function spaces",
      "compressible euler equations",
      "physical vacuum",
      "moving-boundary",
      "well-posedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0910.3136C"
    }
  }
}