The Large Flux Problem to the Navier-Stokes Equations (eBook)

Global Strong Solutions in Cylindrical Domains

Joanna Rencławowicz, Wojciech M. Zajączkowski (Autoren)

eBook Download: PDF

2019 | 1st ed. 2019
VI, 179 Seiten
Springer International Publishing (Verlag)
978-3-030-32330-1 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 9.12.2019
• Reihe/Serie: Advances in Mathematical Fluid Mechanics
• Reihe/Serie: Advances in Mathematical Fluid Mechanics
• Reihe/Serie: Lecture Notes in Mathematical Fluid Mechanics
• Reihe/Serie: Lecture Notes in Mathematical Fluid Mechanics
• Zusatzinfo: VI, 179 p. 3 illus., 1 illus. in color.
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Schlagworte: Anisotropic Sobolev spaces • fluid- and aerodynamics • Fluid flow math • Fluid flow research • Global regular solutions • Global regular solutions with large flux • Incompressible fluid large inflow outflow • incompressible Navier-Stokes equations • Inflow-outflow problem • Inflow-outflow runoff • Large flux Navier-Stokes • Navier-Stokes equation book • Navier-Stokes global strong solution • Partial differential equations • Slip boundary conditions • weak solutions • weighted Sobolev spaces
• ISBN-10: 3-030-32330-7 / 3030323307
• ISBN-13: 978-3-030-32330-1 / 9783030323301