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The Large Flux Problem to the Navier-Stokes Equations
Wojciech M. Zajączkowski, Joanna Rencławowicz
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Springer International Publishing 
Naturwissenschaften, Medizin, Informatik, Technik / Analysis
Beschreibung
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.
Kundenbewertungen
Navier-Stokes equation book, Global regular solutions with large flux, Weighted Sobolev spaces, Global regular solutions, Incompressible Navier-Stokes equations, Inflow-outflow problem, Navier-Stokes global strong solution, Incompressible fluid large inflow outflow, Weak Solutions, Large flux Navier-Stokes, Anisotropic Sobolev spaces, Fluid flow research, Fluid flow math, partial differential equations, fluid- and aerodynamics, Inflow-outflow runoff, Slip boundary conditions