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This authored monograph provides a detailed discussion of the boundary layer flow due to a moving plate. The topical focus lies on the 2- and 3-dimensional case, considering axially symmetric and unsteady flows. The author derives a criterion for the self-similar and non-similar flow, and the turbulent flow due to a stretching or shrinking sheet is also discussed. The target audience primarily comprises research experts in the field of boundary layer flow, but the book will also be beneficial for graduate students.

Leonardo wrote, “Mechanics is the paradise of the mathematical sciences, because by means of it one comes to the fruits of mathematics”; replace “Mechanics” by “Fluid mechanics” and here we are.- From the Preface to the Second EditionAlthough the exponential growth of computer power has advanced the importance of simulations and visualization tools for elaborating new models, designs and technologies, the discipline of fluid mechanics is still large, and turbulence in flows remains a challenging problem in classical physics. Like its predecessor, the revised and expanded Second Edition of this book addresses the basic principles of fluid mechanics and solves fluid flow problems where viscous effects are the dominant physical phenomena.Much progress has occurred in the half a century that has passed since the edition of 1964. As predicted, aspects of hydrodynamics once considered offbeat have risen to importance. For example, the authors have worked on problems where variations in viscosity and surface tension cannot be ignored. The advent of nanotechnology has broadened interest in the hydrodynamics of thin films, and hydromagnetic effects and radiative heat transfer are routinely encountered in materials processing. This monograph develops the basic equations, in the three most important coordinate systems, in a way that makes it easy to incorporate these phenomena into the theory.The book originally described by Prof. Langlois as'a monograph on theoretical hydrodynamics, written in the language of applied mathematics'offers much new coverage including the second principle of thermodynamics, the Boussinesq approximation, time dependent flows, Marangoni convection, Kovasznay flow, plane periodic solutions, Hele-Shaw cells, Stokeslets, rotlets, finite element methods, Wannier flow, corner eddies, and analysis of the Stokes operator.

This book has evolved from lectures and graduate courses given in Brescia (Italy), Bordeaux and Toulouse (France};'It is intended to serve as an intro­ duction to the stability analysis of noncharacteristic multidimensional small viscosity boundary layers developed in (MZl]. We consider parabolic singular perturbations of hyperbolic systems L(u) - £P(u) = 0, where L is a nonlinear hyperbolic first order system and P a nonlinear spatially elliptic term. The parameter e measures the strength of the diffusive effects. With obvious reference to fluid mechanics, it is referred to as a'viscosity.'The equation holds on a domain n and is supplemented by boundary conditions on an.The main goal of this book is to studythe behavior of solutions as etends to O. In the interior of the domain, the diffusive effects are negligible and the nondiffusive or inviscid equations (s = 0) are good approximations. However, the diffusive effects remain important in a small vicinity of the boundary where they induce rapid fluctuations of the solution, called layers. Boundary layers occur in many problems in physics and mechanics. They also occur in free boundary value problems, and in particular in the analysis of shock waves. Indeed, our study of noncharacteristic boundary layers is strongly motivated by the analysis of multidimensional shock waves. At the least, it is a necessary preliminary and important step. We also recall the importance of the viscous approach in the theoretical analysis ofconservation laws (see, e.g., [Lax], (Kru], (Bi-Br]).

It seems doubtful whether we can expect to understand fully the instability of fluid flow without obtaining a mathematical representa­ tion of the motion of a fluid in some particular case in which instability can actually be ob­ served, so that a detailed comparison can be made between the results of analysis and those of experiment. - G.l. Taylor (1923) Though the equations of fluid dynamics are quite complicated, there are configurations which allow simple flow patterns as stationary solutions (e.g. flows between parallel plates or between rotating cylinders). These flow patterns can be obtained only in certain parameter regimes. For parameter values not in these regimes they cannot be obtained, mainly for two different reasons: • The mathematical existence of the solutions is parameter dependent; or • the solutions exist mathematically, but they are not stable. For finding stable steady states, two steps are required: the steady states have to be found and their stability has to bedetermined.