{
  "id": "2204.11001",
  "version": "v1",
  "published": "2022-04-23T06:07:38.000Z",
  "updated": "2022-04-23T06:07:38.000Z",
  "title": "Incompressible limit for a fluid mixture",
  "authors": [
    "Pierre-Etienne Druet"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we discuss the incompressible limit for multicomponent fluids in the isothermal ideal case. Both a direct limit-passage in the equation of state and the low Mach-number limit in rescaled PDEs are investigated. Using the relative energy inequality, we obtain convergence results for the densities and the velocity-field under the condition that the incompressible model possesses a sufficiently smooth solution, which is granted at least for a short time. Moreover, in comparison to single-component flows, uniform estimates and the convergence of the pressure are needed in the multicomponent case because the incompressible velocity field is not divergence-free. We show that certain constellations of the mobility tensor allow to control gradients of the entropic variables and yield the convergence of the pressure in L1.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-23T06:07:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76M45",
      "35Q30",
      "76D05",
      "76N06",
      "76T30"
    ],
    "keywords": [
      "incompressible limit",
      "fluid mixture",
      "isothermal ideal case",
      "low mach-number limit",
      "convergence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}