{
  "id": "2210.10878",
  "version": "v1",
  "published": "2022-10-19T20:37:23.000Z",
  "updated": "2022-10-19T20:37:23.000Z",
  "title": "On the exponential decay in time of solutions to a~generalized Navier-Stokes-Fourier system",
  "authors": [
    "Anna Abbatiello",
    "Miroslav Bulíček",
    "Petr Kaplický"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a non-Newtonian incompressible heat conducting fluid with prescribed nonuniform temperature on the boundary and with the no-slip boundary conditions for the velocity. We assume no external body forces. For the power-law like models with the power law index bigger than $11/5$ in three dimensions, we identify a class of solutions fulfilling the entropy equality and converging to the equilibria exponentially in a proper metric. In fact, we show the existence of a Lyapunov functional for the problem. Consequently, the steady solution is nonlinearly stable and attracts all suitable weak solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-19T20:37:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "35K61",
      "76E30",
      "37L15"
    ],
    "keywords": [
      "exponential decay",
      "navier-stokes-fourier system",
      "power law index bigger",
      "no-slip boundary conditions",
      "non-newtonian incompressible heat conducting fluid"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}