{
  "id": "1304.4562",
  "version": "v1",
  "published": "2013-04-16T19:10:15.000Z",
  "updated": "2013-04-16T19:10:15.000Z",
  "title": "Topology-preserving diffusion of divergence-free vector fields and magnetic relaxation",
  "authors": [
    "Yann Brenier"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The usual heat equation is not suitable to preserve the topology of divergence-free vector fields, because it destroys their integral line structure. On the contrary, in the fluid mechanics literature, on can find examples of topology-preserving diffusion equations for divergence-free vector fields. They are very degenerate since they admit all stationary solutions to the Euler equations of incompressible fluids as equilibrium points. For them, we provide a suitable concept of \"dissipative solutions\", which shares common features with both P.-L. Lions' dissipative solutions to the Euler equations and the concept of \"curves of maximal slopes\", a la De Giorgi, recently used to study the scalar heat equation in very general metric spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-16T19:10:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "divergence-free vector fields",
      "topology-preserving diffusion",
      "magnetic relaxation",
      "euler equations",
      "usual heat equation"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s00220-014-1967-3",
      "journal": "Communications in Mathematical Physics",
      "year": 2014,
      "month": "Sep",
      "volume": 330,
      "number": 2,
      "pages": 757
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014CMaPh.330..757B"
    }
  }
}