{
  "id": "2204.12480",
  "version": "v1",
  "published": "2022-04-26T17:52:34.000Z",
  "updated": "2022-04-26T17:52:34.000Z",
  "title": "Smoothing and Global Attractors for the Hirota-Satsuma System on the Torus",
  "authors": [
    "Engin Başakoğlu",
    "T. Burak Gürel"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the Hirota-Satsuma system, a coupled KdV-type system, with periodic boundary conditions. The first part of the paper concerns with the smoothing estimates for the system. More precisely, it is shown that, for initial data in a Sobolev space, the difference of the nonlinear and linear evolutions lies in a smoother space. The smoothing gain we obtain depends very much on the arithmetic nature of the coupling parameter $a$ which determines the structure of the resonant sets in the estimates. In the second part, we address the forced and damped Hirota-Satsuma system and obtain counterpart smoothing estimates. As a consequence of these estimates, we prove the existence and smoothness of a global attractor in the energy space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-26T17:52:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "global attractor",
      "periodic boundary conditions",
      "smoothing estimates",
      "linear evolutions lies",
      "damped hirota-satsuma system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}