{
  "id": "1911.03944",
  "version": "v1",
  "published": "2019-11-10T15:15:10.000Z",
  "updated": "2019-11-10T15:15:10.000Z",
  "title": "Coercivity for travelling waves in the Gross-Pitaevskii equation in $\\mathbb{R}^2$ for small speed",
  "authors": [
    "David Chiron",
    "Eliot Pacherie"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In a previous paper, we constructed a smooth branch of travelling waves for the 2 dimensional Gross-Pitaevskii equation. Here, we continue the study of this branch. We show some coercivity results, and we deduce from them the kernel of the linearized operator, a spectral stability result, as well as a uniqueness result in the energy space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-10T15:15:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B35",
      "35C07",
      "35Q40",
      "35Q56"
    ],
    "keywords": [
      "travelling waves",
      "dimensional gross-pitaevskii equation",
      "spectral stability result",
      "coercivity results",
      "energy space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}