Mathematical Models in Boundary Layer Theory

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CRC Press, May 25, 1999 - Mathematics - 528 pages
Since Prandtl first suggested it in 1904, boundary layer theory has become a fundamental aspect of fluid dynamics. Although a vast literature exists for theoretical and experimental aspects of the theory, for the most part, mathematical studies can be found only in separate, scattered articles. Mathematical Models in Boundary Layer Theory offers the first systematic exposition of the mathematical methods and main results of the theory.

Beginning with the basics, the authors detail the techniques and results that reveal the nature of the equations that govern the flow within boundary layers and ultimately describe the laws underlying the motion of fluids with small viscosity. They investigate the questions of existence and uniqueness of solutions, the stability of solutions with respect to perturbations, and the qualitative behavior of solutions and their asymptotics. Of particular importance for applications, they present methods for an approximate solution of the Prandtl system and a subsequent evaluation of the rate of convergence of the approximations to the exact solution.

Written by the world's foremost experts on the subject, Mathematical Models in Boundary Layer Theory provides the opportunity to explore its mathematical studies and their importance to the nonlinear theory of viscous and electrically conducting flows, the theory of heat and mass transfer, and the dynamics of reactive and muliphase media. With the theory's importance to a wide variety of applications, applied mathematicians-especially those in fluid dynamics-along with engineers of aeronautical and ship design will undoubtedly welcome this authoritative, state-of-the-art treatise.
 

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Contents

The NavierStokes Equations and the Prandtl System
1
von Mises Variables
20
Crocco Variables
82
Nonstationary Boundary Layer
153
Formation of the Boundary Layer
265
Finite Difference Method
318
Diffraction Problems for the Prandtl System
340
Boundary Layer in NonNewtonian Flows
369
Boundary Layer in Magnetohydrodynamics
456
Homogenization of Boundary Layer Equations
489
Some Open Problems
500
Index
515
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