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The Large Flux Problem to the Navier-Stokes Equations

Global Strong Solutions in Cylindrical Domains

  • Joanna Rencławowicz
  • Wojciech M. Zajączkowski
Book

Part of the Advances in Mathematical Fluid Mechanics book series (AMFM)

Also part of the Lecture Notes in Mathematical Fluid Mechanics book sub series (LNMFM)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Joanna Rencławowicz, Wojciech M. Zajączkowski
    Pages 1-9
  3. Joanna Rencławowicz, Wojciech M. Zajączkowski
    Pages 11-30
  4. Joanna Rencławowicz, Wojciech M. Zajączkowski
    Pages 31-57
  5. Joanna Rencławowicz, Wojciech M. Zajączkowski
    Pages 59-82
  6. Joanna Rencławowicz, Wojciech M. Zajączkowski
    Pages 83-93
  7. Joanna Rencławowicz, Wojciech M. Zajączkowski
    Pages 95-97
  8. Joanna Rencławowicz, Wojciech M. Zajączkowski
    Pages 99-105
  9. Joanna Rencławowicz, Wojciech M. Zajączkowski
    Pages 107-115
  10. Joanna Rencławowicz, Wojciech M. Zajączkowski
    Pages 117-128
  11. Joanna Rencławowicz, Wojciech M. Zajączkowski
    Pages 129-141
  12. Joanna Rencławowicz, Wojciech M. Zajączkowski
    Pages 143-155
  13. Joanna Rencławowicz, Wojciech M. Zajączkowski
    Pages 157-168
  14. Back Matter
    Pages 169-179

About this book

Introduction

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.

Keywords

Incompressible Navier-Stokes equations Incompressible fluid large inflow outflow Global regular solutions with large flux Fluid flow research Fluid flow math Large flux Navier-Stokes Navier-Stokes equation book Navier-Stokes global strong solution Inflow-outflow runoff Slip boundary conditions Global regular solutions Inflow-outflow problem Weighted Sobolev spaces Anisotropic Sobolev spaces Weak Solutions

Authors and affiliations

  • Joanna Rencławowicz
    • 1
  • Wojciech M. Zajączkowski
    • 2
  1. 1.Institute of MathematicsPolish Academy of SciencesWarsawPoland
  2. 2.Institute of Mathematics, Polish Academy of SciencesInstitute of Mathematics and Cryptology, Military University of TechnologyWarsawPoland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-32330-1
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-32329-5
  • Online ISBN 978-3-030-32330-1
  • Series Print ISSN 2297-0320
  • Series Online ISSN 2297-0339
  • Buy this book on publisher's site