{
  "id": "1902.04853",
  "version": "v1",
  "published": "2019-02-13T10:52:24.000Z",
  "updated": "2019-02-13T10:52:24.000Z",
  "title": "On the classification of incompressible fluids and a mathematical analysis of the equations that govern their motion",
  "authors": [
    "Jan Blechta",
    "Josef Málek",
    "K. R. Rajagopal"
  ],
  "categories": [
    "math.AP",
    "physics.flu-dyn"
  ],
  "abstract": "In the first part of the paper we provide a new classification of incompressible fluids characterized by a continuous monotone relation between the velocity gradient and the Cauchy stress. The considered class includes Euler fluids, Navier-Stokes fluids, classical power-law fluids as well as stress power-law fluids, and their various generalizations including the fluids that we refer to as activated fluids, namely fluids that behave as an Euler fluid prior activation and behave as a viscous fluid once activation takes place. We also present a classification concerning boundary conditions that are viewed as the constitutive relations on the boundary. In the second part of the paper, we develop a robust mathematical theory for activated Euler fluids associated with different types of the boundary conditions ranging from no-slip to freeslip and include Navier's slip as well as stick-slip. Both steady and unsteady flows of such fluids in three-dimensional domains are analyzed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-13T10:52:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "76A02",
      "76A05",
      "76D03",
      "35Q35"
    ],
    "keywords": [
      "incompressible fluids",
      "mathematical analysis",
      "euler fluid prior activation",
      "stress power-law fluids",
      "classification concerning boundary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}