{
  "id": "1503.06059",
  "version": "v1",
  "published": "2015-03-20T13:12:20.000Z",
  "updated": "2015-03-20T13:12:20.000Z",
  "title": "New bounds for the inhomogenous Burgers and the Kuramoto-Sivashinsky equations",
  "authors": [
    "Michael Goldman",
    "Marc Josien",
    "Felix Otto"
  ],
  "categories": [
    "math.AP",
    "math.FA"
  ],
  "abstract": "We give a substantially simplified proof of near-optimal estimate on the Kuramoto-Sivashinsky equation from [F. Otto, \"Optimal bounds on the Kuramoto-Sivashinsky equation\", JFA 2009], at the same time slightly improving the result. The result in the above cited paper relied on two ingredients: a regularity estimate for capillary Burgers and an a novel priori estimate for the inhomogeneous inviscid Burgers equation, which works out that in many ways the conservative transport nonlinearity acts as a coercive term. It is the proof of the second ingredient that we substantially simplify by proving a modified K\\'arm\\'an-Howarth-Monin identity for solutions of the inhomogeneous inviscid Burgers equation. This gives a new interpretation of the results obtained in [F. Golse, B. Perthame \"Optimal regularizing effect for scalar conservation laws\", Rev. Mat. Iber., 2013].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-20T13:12:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kuramoto-sivashinsky equation",
      "inhomogenous burgers",
      "inhomogeneous inviscid burgers equation",
      "scalar conservation laws",
      "novel priori estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}