Author : Joanna Rencławowicz
Publisher : Springer Nature
ISBN 13 : 3030323307
Total Pages : 176 pages
Book Rating : 4.0/5 (33 download)
Book Synopsis The Large Flux Problem to the Navier-Stokes Equations by : Joanna Rencławowicz
Download or read book The Large Flux Problem to the Navier-Stokes Equations written by Joanna Rencławowicz and published by Springer Nature. This book was released on 2019-12-09 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.