{
  "id": "1509.03428",
  "version": "v1",
  "published": "2015-09-11T09:08:17.000Z",
  "updated": "2015-09-11T09:08:17.000Z",
  "title": "Strong solutions for two-phase free boundary problems for a class of non-Newtonian fluids",
  "authors": [
    "Matthias Hieber",
    "Hirokazu Saito"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Consider the two-phase free boundary problem subject to surface tension and gravitational forces for a class of non-Newtonian fluids with stress tensors $T_i$ of the form $T_i=-\\pi I+\\mu_i(|D(v)|^2)D(v)$ for $i=1,2$, respectively, and where the viscosity functions $\\mu_i$ satisfy $\\mu_i(s)\\in C^3([0,\\infty))$ and $\\mu_i(0)>0$ for $i=1,2$. It is shown that for given $T>0$ this problem admits a unique, strong solution on $(0,T)$ provided the initial data are sufficiently small in their natural norms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-11T09:08:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-newtonian fluids",
      "strong solution",
      "two-phase free boundary problem subject",
      "surface tension",
      "gravitational forces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150903428H"
    }
  }
}