{
  "id": "1709.04713",
  "version": "v1",
  "published": "2017-09-14T11:34:29.000Z",
  "updated": "2017-09-14T11:34:29.000Z",
  "title": "Classical well-posedness in dispersive equations with nonlinearities of mild regularity, and a composition theorem in Besov spaces",
  "authors": [
    "Mats Ehrnström",
    "Long Pei"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "For both localized and periodic initial data, we prove local existence in classical energy space $H^s, s>\\frac{3}{2}$, for a class of dispersive equations $u_{t}+(n(u))_{x}+Lu_{x}=0$ with nonlinearities of mild regularity. Our results are valid for symmetric Fourier multiplier operators $L$ whose symbol is of temperate growth, and $n(\\cdot)$ in local Sobolev space $H^{s+2}_{\\mathrm{loc}}(\\mathbb{R})$. In particular, the results include non-smooth and exponentially growing nonlinearities. Our proof is based on a combination of semi-group methods and a new composition result for Besov spaces. In particular, we extend a previous result for Nemytskii operators on Besov spaces on $\\mathbb{R}$ to the periodic setting by using the difference-derivative characterization of Besov spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-14T11:34:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "47J35",
      "35Q53",
      "45J05",
      "76B15"
    ],
    "keywords": [
      "besov spaces",
      "mild regularity",
      "dispersive equations",
      "composition theorem",
      "classical well-posedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}