{
  "id": "math/0212116",
  "version": "v2",
  "published": "2002-12-09T06:32:49.000Z",
  "updated": "2003-03-12T07:42:30.000Z",
  "title": "Unique solvability of the free-boundary Navier-Stokes equations with surface tension",
  "authors": [
    "Daniel Coutand",
    "Steve Shkoller"
  ],
  "comment": "73 pages; typos corrected; minor details added",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the existence and uniqueness of solutions to the time-dependent incompressible Navier-Stokes equations with a free-boundary governed by surface tension. The solution is found using a topological fixed-point theorem for a nonlinear iteration scheme, requiring at each step, the solution of a model linear problem consisting of the time-dependent Stokes equation with linearized mean-curvature forcing on the boundary. We use energy methods to establish new types of spacetime inequalities that allow us to find a unique weak solution to this problem. We then prove regularity of the weak solution, and establish the a priori estimates required by the nonlinear iteration process.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2003-03-12T07:42:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "76D03",
      "76B45"
    ],
    "keywords": [
      "free-boundary navier-stokes equations",
      "surface tension",
      "unique solvability",
      "time-dependent stokes equation",
      "nonlinear iteration scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 73,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....12116C"
    }
  }
}