{
  "id": "1107.1823",
  "version": "v2",
  "published": "2011-07-09T22:39:24.000Z",
  "updated": "2011-07-12T03:28:23.000Z",
  "title": "On the Local Well-posedness of a 3D Model for Incompressible Navier-Stokes Equations with Partial Viscosity",
  "authors": [
    "Thomas Y. Hou",
    "Zuoqiang Shi",
    "Shu Wang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this short note, we study the local well-posedness of a 3D model for incompressible Navier-Stokes equations with partial viscosity. This model was originally proposed by Hou-Lei in \\cite{HouLei09a}. In a recent paper, we prove that this 3D model with partial viscosity will develop a finite time singularity for a class of initial condition using a mixed Dirichlet Robin boundary condition. The local well-posedness analysis of this initial boundary value problem is more subtle than the corresponding well-posedness analysis using a standard boundary condition because the Robin boundary condition we consider is non-dissipative. We establish the local well-posedness of this initial boundary value problem by designing a Picard iteration in a Banach space and proving the convergence of the Picard iteration by studying the well-posedness property of the heat equation with the same Dirichlet Robin boundary condition.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-12T03:28:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local well-posedness",
      "incompressible navier-stokes equations",
      "dirichlet robin boundary condition",
      "3d model",
      "partial viscosity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1107.1823H"
    }
  }
}