{
  "id": "1708.00086",
  "version": "v1",
  "published": "2017-07-31T22:12:20.000Z",
  "updated": "2017-07-31T22:12:20.000Z",
  "title": "A priori estimates for the free-boundary Euler equations with surface tension in three dimensions",
  "authors": [
    "Marcelo M. Disconzi",
    "Igor Kukavica"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We derive a priori estimates for the incompressible free-boundary Euler equations with surface tension in three spatial dimensions. Working in Lagrangian coordinates, we provide a priori estimates for the local existence when the initial velocity, which is rotational, belongs to $H^3$ and the trace of initial velocity on the free boundary to $H^{3.5}$, thus lowering the requirement on the regularity of initial data in the Lagrangian setting. Our methods are direct and involve three key elements: estimates for the pressure, the boundary regularity provided by the mean curvature, and the Cauchy invariance.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-31T22:12:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "priori estimates",
      "surface tension",
      "initial velocity",
      "incompressible free-boundary euler equations",
      "free boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}