{
  "id": "1509.06867",
  "version": "v1",
  "published": "2015-09-23T07:39:38.000Z",
  "updated": "2015-09-23T07:39:38.000Z",
  "title": "Blow-up Criteria for the Three Dimensional Nonlinear Dissipative System Modeling Electro-hydrodynamics",
  "authors": [
    "Jihong Zhao",
    "Meng Bai"
  ],
  "comment": "21 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we investigate some sufficient conditions for the breakdown of local smooth solutions to the three dimensional nonlinear nonlocal dissipative system modeling electro-hydrodynamics. This model is a strongly coupled system by the well-known incompressible Navier-Stokes equations and the classical Poisson-Nernst-Planck equations. We show that the maximum of the vorticity field alone controls the breakdown of smooth solutions, which reveals that the velocity field plays a more dominant role than the density functions of charged particles in the blow-up theory of the system. Moreover, some Prodi-Serrin type blow-up criteria are also established.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-23T07:39:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B44",
      "35K55",
      "35Q35"
    ],
    "keywords": [
      "nonlinear dissipative system modeling electro-hydrodynamics",
      "dimensional nonlinear dissipative system modeling",
      "blow-up criteria",
      "nonlinear nonlocal dissipative system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}