{
  "id": "2010.12261",
  "version": "v1",
  "published": "2020-10-23T09:41:01.000Z",
  "updated": "2020-10-23T09:41:01.000Z",
  "title": "The Muskat problem with surface tension and equal viscosities in subcritical $L_p$-Sobolev spaces",
  "authors": [
    "Anca-Voichita Matioc",
    "Bogdan-Vasile Matioc"
  ],
  "comment": "29 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we establish the well-posedness of the Muskat problem with surface tension and equal viscosities in the subcritical Sobolev spaces $W^s_p(\\mathbb{R})$, where ${p\\in(1,2]}$ and ${s\\in(1+1/p,2)}$. This is achieved by showing that the mathematical model can be formulated as a quasilinear parabolic evolution problem in $W^{\\overline{s}-2}_p(\\mathbb{R})$, where ${\\overline{s}\\in(1+1/p,s)}$. Moreover, we prove that the solutions become instantly smooth and we provide a criterion for the global existence of solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-23T09:41:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R37",
      "76D27",
      "35K59"
    ],
    "keywords": [
      "surface tension",
      "equal viscosities",
      "muskat problem",
      "quasilinear parabolic evolution problem",
      "subcritical sobolev spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}