{
  "id": "2408.07141",
  "version": "v1",
  "published": "2024-08-13T18:19:52.000Z",
  "updated": "2024-08-13T18:19:52.000Z",
  "title": "Rigid body in compressible flow with general inflow-outflow boundary data",
  "authors": [
    "Šimon Axmann",
    "Šárka Nečasová",
    "Ana Radošević"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the motion of a rigid body within a compressible, isentropic, and viscous fluid contained in a fixed bounded domain $\\Omega \\subset \\mathbb{R}^3$. The fluid's behavior is described by the Navier-Stokes equations, while the motion of the rigid body is governed by ordinary differential equations representing the conservation of linear and angular momentum. We prescribe a time-independent fluid velocity along the boundary of $\\Omega$ and a time-independent fluid density at the inflow boundary of $\\Omega$. Additionally, we assume a no-slip boundary condition at the interface between the fluid and the rigid body. We prove existence of a weak solution to the given problem within a time interval where the rigid body does not touch the boundary $\\partial\\Omega$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-13T18:19:52.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rigid body",
      "general inflow-outflow boundary data",
      "compressible flow",
      "no-slip boundary condition",
      "time-independent fluid density"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}