{
  "id": "2102.06926",
  "version": "v1",
  "published": "2021-02-13T13:09:46.000Z",
  "updated": "2021-02-13T13:09:46.000Z",
  "title": "On long-time behavior of solutions of the Zakharov-Rubenchik/Benney-Roskes system",
  "authors": [
    "María E. Martínez",
    "José M. Palacios"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study decay properties for solutions to the initial value problem associated with the one-dimensional Zakharov-Rubenchik/Benney-Roskes system. We prove time-integrability in growing compact intervals of size $t^{r}$, $r<2/3$, centered on some characteristic curves coming from the underlying transport equations associated with the ZR/BR system. Additionally, we prove decay to zero of the local energy-norm in so-called far-field regions. Our results are independent of the size of the initial data and do not require any parity condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-13T13:09:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "long-time behavior",
      "study decay properties",
      "initial value problem",
      "one-dimensional zakharov-rubenchik/benney-roskes system",
      "parity condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}