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:
    non sort: The
    title: Large Flux Problem to the Navier-Stokes Equations
    sub title: Global Strong Solutions in Cylindrical Domains
  name:
    name part: Rencławowicz, Joanna.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Zajączkowski, Wojciech M.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2019
    edition: 1st ed. 2019.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: VI, 179 p. 3 illus., 1 illus. in color. online resource.
  abstract: This monograph considers the motion of incompressible fluids described by the Navier-Stokes equations with large inflow and outflow, and proves the existence of global regular solutions without any restrictions on the magnitude of the initial velocity, the external force, or the flux. To accomplish this, some assumptions are necessary: The flux is close to homogeneous, and the initial velocity and the external force do not change too much along the axis of the cylinder. This is achieved by utilizing a sophisticated method of deriving energy type estimates for weak solutions and global estimates for regular solutions-an approach that is wholly unique within the existing literature on the Navier-Stokes equations. To demonstrate these results, three main steps are followed: first, the existence of weak solutions is shown; next, the conditions guaranteeing the regularity of weak solutions are presented; and, lastly, global regular solutions are proven. This volume is ideal for mathematicians whose work involves the Navier-Stokes equations, and, more broadly, researchers studying fluid mechanics.
  table of contents: Introduction -- Notation and auxiliary results -- Energy estimate: Global weak solutions -- Local estimates for regular solutions -- Global estimates for solutions to problem on (v, p) -- Global estimates for solutions to problem on (h, q) -- Estimates for ht -- Auxiliary results: Estimates for (v, p) -- Auxiliary results: Estimates for (h, q) -- The Neumann problem (3.6) in L2-weighted spaces -- The Neumann problem (3.6) in Lp-weighted spaces -- Existence of solutions (v, p) and (h, q).
  note: by Joanna Rencławowicz, Wojciech M. Zajączkowski.
  subject:
    topic: Partial differential equations
  subject:
    topic: Fluids
  subject:
    topic: Functional analysis
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Fluid- and Aerodynamics
  subject:
    topic: Functional Analysis
  classification: QA370-380
  classification: 515.353
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes in Mathematical Fluid Mechanics
  identifier: 9783030323301
  identifier: https://doi.org/10.1007/978-3-030-32330-1
  record info:
    record creation date: 191209
    record change date: 20191210141425.0
    record identifier: 978-3-030-32330-1