{
  "id": "1206.1457",
  "version": "v2",
  "published": "2012-06-07T11:51:12.000Z",
  "updated": "2012-06-09T07:06:45.000Z",
  "title": "Global well-posedness and stability of electro-kinetic flows",
  "authors": [
    "Dieter Bothe",
    "André Fischer",
    "Jürgen Saal"
  ],
  "comment": "61 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a coupled system of Navier-Stokes and Nernst-Planck equations, describing the evolution of the velocity and the concentration fields of dissolved constituents in an electrolyte solution. Motivated by recent applications in the field of micro- and nanofluidics, we consider the model in such generality that electrokinetic flows are included. This prohibits employing the assumption of electroneutrality of the total solution, which is a common approach in the mathematical literature in order to determine the electrical potential. Therefore we complement the system of mass and momentum balances with a Poisson equation for the electrostatic potential, with the charge density stemming from the concentrations of the ionic species. For the resulting Navier-Stokes-Nernst-Planck-Poisson system we prove the existence of unique local strong solutions in bounded domains in $\\R^n$ for any $n\\geq2$ as well as the existence of unique global strong solutions and exponential convergence to uniquely determined steady states in two dimensions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-09T07:06:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76E25",
      "76D05",
      "35B25",
      "35K51"
    ],
    "keywords": [
      "global well-posedness",
      "electro-kinetic flows",
      "unique local strong solutions",
      "unique global strong solutions",
      "momentum balances"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 61,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.1457B"
    }
  }
}