{
  "id": "2003.14267",
  "version": "v1",
  "published": "2020-03-31T14:52:20.000Z",
  "updated": "2020-03-31T14:52:20.000Z",
  "title": "Sharp Interface Limit of a Stokes/Cahn-Hilliard System, Part II: Approximate Solutions",
  "authors": [
    "Helmut Abels",
    "Andreas Marquardt"
  ],
  "comment": "59 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We construct rigorously suitable approximate solutions to the Stokes/Cahn-Hilliard system by using the method of matched asymptotics expansions. This is a main step in the proof of convergence given in the first part of this contribution, where the rigorous sharp interface limit of a coupled Stokes/Cahn-Hilliard system in a two dimensional, bounded and smooth domain is shown. As a novelty compared to earlier works, we introduce fractional order terms, which are of significant importance, but share the problematic feature that they may not be uniformly estimated in $\\epsilon$ in arbitrarily strong norms. As a consequence, gaining necessary estimates for the error, which occurs when considering the approximations in the Stokes/Cahn-Hilliard system, is rather involved.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-31T14:52:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76T99",
      "35Q30",
      "35Q35",
      "35R35",
      "76D05",
      "76D45"
    ],
    "keywords": [
      "stokes/cahn-hilliard system",
      "fractional order terms",
      "rigorous sharp interface limit",
      "construct rigorously suitable approximate solutions",
      "earlier works"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}