{
  "id": "1201.1986",
  "version": "v2",
  "published": "2012-01-10T08:47:25.000Z",
  "updated": "2012-01-17T03:45:52.000Z",
  "title": "Vanishing Viscous Limits for 3D Navier-Stokes Equations with A Navier-Slip Boundary Condition",
  "authors": [
    "Lizhen Wang",
    "Zhouping Xin",
    "Aibin Zang"
  ],
  "comment": "45pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we investigate the vanishing viscosity limit for solutions to the Navier-Stokes equations with a Navier slip boundary condition on general compact and smooth domains in $\\mathbf{R}^3$. We first obtain the higher order regularity estimates for the solutions to Prandtl's equation boundary layers. Furthermore, we prove that the strong solution to Navier-Stokes equations converges to the Eulerian one in $C([0,T];H^1(\\Omega))$ and $L^\\infty((0,T)\\times\\o)$, where $T$ is independent of the viscosity, provided that initial velocity is regular enough. Furthermore, rates of convergence are obtained also.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-17T03:45:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "35Q35"
    ],
    "keywords": [
      "3d navier-stokes equations",
      "navier-slip boundary condition",
      "vanishing viscous limits",
      "navier slip boundary condition",
      "higher order regularity estimates"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00021-012-0103-4",
      "journal": "Journal of Mathematical Fluid Mechanics",
      "year": 2012,
      "month": "Dec",
      "volume": 14,
      "number": 4,
      "pages": 791
    },
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012JMFM...14..791W"
    }
  }
}