{
  "id": "2301.04080",
  "version": "v1",
  "published": "2023-01-10T17:11:30.000Z",
  "updated": "2023-01-10T17:11:30.000Z",
  "title": "Null Controllability of One-Dimensional Linearized Compressible Navier-Stokes System in Periodic Setup Using One Boundary Control",
  "authors": [
    "Jiten Kumbhakar"
  ],
  "categories": [
    "math.AP",
    "math.OC"
  ],
  "abstract": "In this article, we study boundary null controllability properties of the linearized compressible Navier-Stokes equations in one dimension for both barotropic and non-barotropic fluids using only one boundary control. The control acts through periodic boundary conditions. We prove null controllability of the linearized compressible Navier-Stokes system (for both barotropic and non-barotropic fluids) at large time $T$. We also prove that our result is sharp with respect to the regularity of the initial states. Finally, for both barotropic and non-barotropic fluids, we prove a lack of controllability at small time $T$ when a control acts in density.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-10T17:11:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "one-dimensional linearized compressible navier-stokes system",
      "boundary control",
      "periodic setup",
      "non-barotropic fluids",
      "study boundary null controllability properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}