The Large Flux Problem to the Navier-Stokes Equations

Global Strong Solutions in Cylindrical Domains

Joanna Rencławowicz, Wojciech M. Zajączkowski (Autoren)

Buch | Softcover

VI, 179 Seiten

2019 | 1st ed. 2019
Springer International Publishing (Verlag)
978-3-030-32329-5 (ISBN)

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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.

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 h_t.-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).

Erscheinungsdatum	12.12.2019
Reihe/Serie	Advances in Mathematical Fluid Mechanics
Reihe/Serie	Lecture Notes in Mathematical Fluid Mechanics
Zusatzinfo	VI, 179 p. 3 illus., 1 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	296 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik
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	3-030-32329-3 / 3030323293
ISBN-13	978-3-030-32329-5 / 9783030323295
Zustand	Neuware