{
  "id": "1812.06260",
  "version": "v1",
  "published": "2018-12-15T09:17:38.000Z",
  "updated": "2018-12-15T09:17:38.000Z",
  "title": "Global strong solutions to 3-D Navier-Stokes system with strong dissipation in one direction",
  "authors": [
    "Marius Paicu",
    "Ping Zhang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider three dimensional incompressible Navier-Stokes equation $(NS)$ with different viscous coefficient in the vertical and horizontal variables. In particular, when one of these viscous coefficients is large enough compared to the initial data, we prove the global well-posedness of this system. In fact, we obtain the existence of a global strong solution to $(NS)$ when the initial data verify an anisotropic smallness condition which takes into account the different roles of the horizontal and vertical viscosity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-15T09:17:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global strong solution",
      "strong dissipation",
      "navier-stokes system",
      "initial data",
      "dimensional incompressible navier-stokes equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}