{
  "id": "2405.11900",
  "version": "v1",
  "published": "2024-05-20T09:31:19.000Z",
  "updated": "2024-05-20T09:31:19.000Z",
  "title": "Global-in-time well-posedness of the compressible Navier-Stokes equations with striated density",
  "authors": [
    "Xian Liao",
    "Sagbo Marcel Zodji"
  ],
  "comment": "35 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We first show local-in-time well-posedness of the compressible Navier-Stokes equations, assuming striated regularity while no other smoothness or smallness conditions on the initial density. With these local-in-time solutions served as blocks, for \\textit{less} regular initial data where the vacuum is permitted, the global-in-time well-posedness follows from the energy estimates and the propagated striated regularity of the density function, if the bulk viscosity coefficient is large enough in the two dimensional case. The global-in-time well-posedness holds also true in the three dimensional case, provided with large bulk viscosity coefficient together with small initial energy. This solves the density-patch problem in the exterior domain for the compressible model with $W^{2,p}$-Interfaces. Finally, the singular incompressible limit toward the inhomogenous incompressible model when the bulk viscosity coefficient tends to infinity is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-20T09:31:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35A02",
      "35Q30",
      "35R35",
      "76N10"
    ],
    "keywords": [
      "compressible navier-stokes equations",
      "striated density",
      "dimensional case",
      "large bulk viscosity coefficient",
      "bulk viscosity coefficient tends"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}