{
  "id": "1910.09828",
  "version": "v1",
  "published": "2019-10-22T08:28:48.000Z",
  "updated": "2019-10-22T08:28:48.000Z",
  "title": "Stability of a class of semilinear waves in $2+1$ dimension under null condition",
  "authors": [
    "Shijie Dong"
  ],
  "comment": "13 pages, all comments are welcome",
  "categories": [
    "math.AP"
  ],
  "abstract": "Under the classical null condition, semilinear wave equations with quadratic nonlinearities in $\\RR^{2+1}$ might not have global-in-time solutions. We will show that in $\\RR^{2+1}$ semilinear wave equations of the form $-\\Box u = u Q(\\del u; \\del u)$ possess global-in-time solutions if the null condition on $Q(\\del u; \\del u)$ is assumed. As a consequence, we also provide a new proof, after \\cite{Wong}, on the small data global solutions to the wave map equation in $\\RR^{2+1}$ and no compactness assumptions on the initial data are needed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-22T08:28:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "null condition",
      "semilinear wave equations",
      "small data global solutions",
      "wave map equation",
      "possess global-in-time solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}