{
  "id": "2010.05520",
  "version": "v1",
  "published": "2020-10-12T08:22:29.000Z",
  "updated": "2020-10-12T08:22:29.000Z",
  "title": "Long time behavior of solutions for a damped Benjamin-Ono equation",
  "authors": [
    "Louise Gassot"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Benjamin-Ono equation on the torus with an additional damping term on the smallest Fourier modes (cos and sin). We first prove global well-posedness of this equation in $L^2_{r,0}(\\mathbb{T})$. Then, we describe the weak limit points of the trajectories in $L^2_{r,0}(\\mathbb{T})$ when time goes to infinity, and show that these weak limit points are strong limit points. Finally, we prove the boundedness of higher-order Sobolev norms for this equation. Our key tool is the Birkhoff map for the Benjamin-Ono equation, that we use as an adapted nonlinear Fourier transform.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-12T08:22:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "long time behavior",
      "damped benjamin-ono equation",
      "weak limit points",
      "strong limit points",
      "adapted nonlinear fourier transform"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}