{
  "id": "2210.16950",
  "version": "v1",
  "published": "2022-10-30T21:21:04.000Z",
  "updated": "2022-10-30T21:21:04.000Z",
  "title": "On the Motion of a Pendulum with a Cavity Filled with a Compressible Fluid",
  "authors": [
    "Giovanni Paolo Galdi",
    "Václav Mácha",
    "Šárka Nečasová",
    "Bangwei She"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study the motion of the coupled system, $\\mathscr S$, constituted by a physical pendulum, $\\mathscr B$, with an interior cavity entirely filled with a viscous, compressible fluid, $\\mathscr F$. The presence of the fluid may strongly affect on the motion of $\\mathscr B$. In fact, we prove that, under appropriate assumptions, the fluid acts as a damper, namely, $\\mathscr S$ must eventually reach a rest-state. Such a state is characterized by a suitable time-independent density distribution of $\\mathscr F$ and a corresponding equilibrium position of the center of mass of $\\mathscr S$. These results are proved in the very general class of weak solutions and do not require any restriction on the initial data, other than having a finite energy. We complement our findings with some numerical tests. The latter show, among other things, the interesting property that ``large\" compressibility favors the damping effect, since it drastically reduces the time that $\\mathscr S$ takes to go to rest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-30T21:21:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compressible fluid",
      "suitable time-independent density distribution",
      "initial data",
      "weak solutions",
      "general class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}