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The Large Flux Problem to the Navier-Stokes Equations: Global Strong Solutions in Cylindrical Domains (Lecture Notes in Mathematical Fluid Mechanics) - Softcover

Buch 15 von 21: Advances in Mathematical Fluid Mechanics

Rencławowicz, Joanna; Zajączkowski, Wojciech M.

 
9783030323295: The Large Flux Problem to the Navier-Stokes Equations: Global Strong Solutions in Cylindrical Domains (Lecture Notes in Mathematical Fluid Mechanics)
Softcover
ISBN 10: 3030323293 ISBN 13: 9783030323295
Verlag: Birkhäuser, 2019

Inhaltsangabe

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.

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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.

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Verlag
Birkhäuser
Erscheinungsdatum
2019
Sprache
Englisch
ISBN 10 
3030323293
ISBN 13 
9783030323295
Einband
Taschenbuch
Auflage
1
Anzahl der Seiten
188
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Weitere beliebte Ausgaben desselben Titels

9783030323318: The Large Flux Problem to the Navier-Stokes Equations: Global Strong Solutions in Cylindrical Domains

Vorgestellte Ausgabe

ISBN 10:  3030323315 ISBN 13:  9783030323318
Verlag: Birkhäuser, 2019
Softcover