rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow
  name:
    name part: Bellout, Hamid.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Bloom, Frederick.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XX, 569 p. 16 illus. online resource.
  abstract: The theory of incompressible multipolar viscous fluids is a non-Newtonian model of fluid flow, which incorporates nonlinear viscosity, as well as higher order velocity gradients, and is based on scientific first principles. The Navier-Stokes model of fluid flow is based on the Stokes hypothesis, which a priori simplifies and restricts the relationship between the stress tensor and the velocity. By relaxing the constraints of the Stokes hypothesis, the mathematical theory of multipolar viscous fluids generalizes the standard Navier-Stokes model. The rigorous theory of multipolar viscous fluids is compatible with all known thermodynamical processes and the principle of material frame indifference; this is in contrast with the formulation of most non-Newtonian fluid flow models which result from ad hoc assumptions about the relation between the stress tensor and the velocity. The higher-order boundary conditions, which must be formulated for multipolar viscous flow problems, are a rigorous consequence of the principle of virtual work; this is in stark contrast to the approach employed by authors who have studied the regularizing effects of adding artificial viscosity, in the form of higher order spatial derivatives, to the Navier-Stokes model. A number of research groups, primarily in the United States, Germany, Eastern Europe, and China, have explored the consequences of multipolar viscous fluid models; these efforts, and those of the authors, which are described in this book, have focused on the solution of problems in the context of specific geometries, on the existence of weak and classical solutions, and on dynamical systems aspects of the theory. This volume will be a valuable resource for mathematicians interested in solutions to systems of nonlinear partial differential equations, as well as to applied mathematicians, fluid dynamicists, and mechanical engineers with an interest in the problems of fluid mechanics.
  table of contents: Preface -- Acknowledgements -- I Incompressible Multipolar Fluid Dynamics -- II Plane Poiseuille Flow of Incompressible Bipolar Viscous Fluids -- III Incompressible Bipolar Fluid Dynamics: Examples of Other Flows and Geometries -- IV General Existence and Uniqueness Theorems for Incompressible Bipolar and non-Newtonian Fluid Flow -- V Attractors for Incompressible Bipolar and non-Newtonian Flows: Bounded Domains and Space Periodic Problems -- VI Inertial Manifolds, Orbit Squeezing, and Attractors for Bipolar Flow in Unbounded Channels -- A.I Notation, Definitions, and Results from Analysis -- A.II Estimates Involving the Rate of Deformation Tensor -- A.III The Spectral Gap Condition -- Bibliography -- Index.
  note: by Hamid Bellout, Frederick Bloom.
  subject:
    topic: Mathematics
  subject:
    topic: Partial differential equations
  subject:
    topic: Mathematical physics
  subject:
    topic: Fluids
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical Physics
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Fluid- and Aerodynamics
  classification: QA401-425
  classification: QC19.2-20.85
  classification: 530.15
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Advances in Mathematical Fluid Mechanics
  identifier: 9783319008912
  identifier: http://dx.doi.org/10.1007/978-3-319-00891-2
  record info:
    record creation date: 131113
    record change date: 20151031101022.0
    record identifier: 978-3-319-00891-2