{
  "id": "1707.03096",
  "version": "v1",
  "published": "2017-07-11T01:34:13.000Z",
  "updated": "2017-07-11T01:34:13.000Z",
  "title": "Global solvability of the Navier-Stokes equations with a free surface in the maximal $L_p\\text{-}L_q$ regularity class",
  "authors": [
    "Hirokazu Saito"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the motion of incompressible viscous fluids bounded above by a free surface and below by a solid surface in the $N$-dimensional Euclidean space for $N\\geq 2$ when the gravity is not taken into account. The aim of this paper is to show the global solvability of the Naiver-Stokes equations with a free surface, describing the above-mentioned motion, in the maximal $L_p\\text{-}L_q$ regularity class. Our approach is based on the maximal $L_p\\text{-}L_q$ regularity with exponential stability for the linearized equations, and solutions to the original nonlinear problem are also exponentially stable.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-11T01:34:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free surface",
      "global solvability",
      "regularity class",
      "navier-stokes equations",
      "dimensional euclidean space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}