The Steady Navier-Stokes System

This book provides a successful solution to one of the central problems of mathematical fluid mechanics: the Lerays problem on existence of a solution to the boundary value problem for the stationary NavierStokes system in bounded domains under sole condition of zero total flux. This marks the culmination of the authors' work over the past few years on this under-explored topic within the study of the NavierStokes equations. This book will be the first major work on the NavierStokes equations to explore Lerays problem in detail. The results are presented with detailed proofs, as are the history of the problem and the previous approaches to finding a solution to it. In addition, for the readers convenience and for the self-sufficiency of the text, the foundations of the mathematical theory for incompressible fluid flows described by the steady state Stokes and NavierStokes systems are presented. For researchers in this active area, this book will be a valuable resource.