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Lecture Notes in Mathematical Fluid Mechanics

The Large Flux Problem to the Navier-Stokes Equations

Global Strong Solutions in Cylindrical Domains

Authors: Rencławowicz, Joanna, Zajączkowski, Wojciech M.

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  • Considers the motion of incompressible fluids described by the Navier-Stokes equations with large inflow and outflow
  • Proves global existence of regular solutions without any restrictions on the magnitude of the initial velocity, the external force, or the flux
  • Utilizes a sophisticated method of increasing regularity of weak solutions through an application of weighted Sobolev spaces
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About this book

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 (12 chapters)

Table of contents (12 chapters)

Buy this book

eBook 50,28 €
price for Spain (gross)
  • ISBN 978-3-030-32330-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-030-32329-5
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
The Large Flux Problem to the Navier-Stokes Equations
Book Subtitle
Global Strong Solutions in Cylindrical Domains
Authors
Series Title
Lecture Notes in Mathematical Fluid Mechanics
Copyright
2019
Publisher
Birkhäuser Basel
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-32330-1
DOI
10.1007/978-3-030-32330-1
Softcover ISBN
978-3-030-32329-5
Series ISSN
2510-1374
Edition Number
1
Number of Pages
VI, 179
Number of Illustrations
2 b/w illustrations, 1 illustrations in colour
Topics

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