{
  "id": "1303.6148",
  "version": "v2",
  "published": "2013-03-25T14:53:18.000Z",
  "updated": "2013-08-06T12:14:10.000Z",
  "title": "On the Radius of Analyticity of Solutions to the Cubic Szegö Equation",
  "authors": [
    "Patrick Gerard",
    "Yanqiu Guo",
    "Edriss S. Titi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is concerned with the cubic Szeg\\H{o} equation $$ i\\partial_t u=\\Pi(|u|^2 u), $$ defined on the $L^2$ Hardy space on the one-dimensional torus $\\mathbb T$, where $\\Pi: L^2(\\mathbb T)\\rightarrow L^2_+(\\mathbb T)$ is the Szeg\\H{o} projector onto the non-negative frequencies. For analytic initial data, it is shown that the solution remains spatial analytic for all time $t\\in (-\\infty,\\infty)$. In addition, we find a lower bound for the radius of analyticity of the solution. Our method involves energy-like estimates of the special Gevrey class of analytic functions based on the $\\ell^1$ norm of Fourier transforms (the Wiener algebra).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-08-06T12:14:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B10",
      "35B65",
      "47B35"
    ],
    "keywords": [
      "analyticity",
      "solution remains spatial analytic",
      "special gevrey class",
      "analytic initial data",
      "wiener algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.6148G"
    }
  }
}