{
  "id": "1807.04044",
  "version": "v1",
  "published": "2018-07-11T09:53:46.000Z",
  "updated": "2018-07-11T09:53:46.000Z",
  "title": "Strong convergence of a vector-BGK model to the incompressible Navier-Stokes equations via the relative entropy method",
  "authors": [
    "Roberta Bianchini"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The aim of this paper is to prove the strong convergence of the solutions to a vector-BGK model under the diffusive scaling to the incompressible Navier-Stokes equations on the two-dimensional torus. This result holds in any interval of time $[0, T]$, with $T>0$. We also provide the global in time uniform boundedness of the solutions to the approximating system. Our argument is based on the use of local in time $H^s$-estimates for the model, established in a previous work, combined with the $L^2$-relative entropy estimate and the interpolation properties of the Sobolev spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-11T09:53:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "incompressible navier-stokes equations",
      "relative entropy method",
      "strong convergence",
      "vector-bgk model",
      "time uniform boundedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}