Mathematical Models in Boundary Layer Theory / Edition 1

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Overview

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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Editorial Reviews

Booknews
This book provides a thorough exposition of results and mathematical methods in boundary layer theory. The existence and uniqueness theorems under natural assumptions on the data are proven for Prandtl's boundary layer equations and their generalizations. The book also considers the asymptotic behaviors of the solutions of boundary layer equations, and many other mathematical problems. It is intended for researchers in the aircraft and ship-building industries, as well as students in mathematics, mechanics, and engineering. Oleinik is head of the Department of Differential Equations at the Faculty of mathematics and Mechanics of Moscow State University. Samokhin teaches mathematics at Moscow State University. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781584880158
  • Publisher: Taylor & Francis
  • Publication date: 5/25/1999
  • Series: Applied Mathematics Series , #15
  • Edition number: 1
  • Pages: 528
  • Product dimensions: 6.40 (w) x 9.40 (h) x 1.30 (d)

Table of Contents

The Navier-Stokes Equations and Prandtl
Derivation of the Prandtl System
Solution of the Boundary Layer System as the First Approximation to Asymptotic Solution of the Navier-Stokes Equations near the Boundary
Separation of the Boundary Layer
Setting of the Main Problems for the Equations of Boundary Layer
Boundary Layer Equations for Non-Newtonian Fluids
Boundary Layers in Magnetohydrodynamics
Stationary Boundary Layer: von Mises Variables
Continuation of Two-Dimensional Boundary Layer
Asymptotic Behavior of the Velocity Component along the Boundary Layer
Conditions for Boundary Layer Separation
Self-Similar Solutions of the Boundary Layer Equations
Solving the Continuation Problem by the Line Method
On Three-Dimensional Boundary Layer Equations
Comments
Stationary Boundary Layer: Crocco Variables
Axially Symmetric Stationary Boundary Layer
Symmetric Boundary Layer
The Problem of Continuation of the Boundary Layer
Weak Solutions of the Boundary Layer System
Nonstationary Boundary Layer
Axially Symmetric Boundary Layer
The Continuation Problem for a Nonstationary Axially Symmetric Boundary Layer
Continuation of the Boundary Layer: Successive Approximations
On t-Global Solutions of the Prandtl System for Axially Symmetric Flows
Stability of Solutions of the Prandtl System
Time-Periodic Solutions of the Nonstationary Boundary Layer System
Solving the Nonstationary Prandtl System by the Line Method in the Time Variable
Formation of the Boundary Layer
Solutions and Asymptotic Expansions for the Problem of Boundary Layer formation: The Case of Gradual Acceleration
Formation of the Boundary Layer about a Body that Suddenly Starts to Move
Comments
Finite-Difference Method
Solving the Boundary Layer Continuation Problem by the Finite Difference Method
Solving the Prandtl System for Axially Symmetric Flows by the Finite Difference Method
Comments
Diffraction Problems for the Prandtl System
Boundary Layer with Unknown Border between Two media
Mixing of Two Fluids with Distinct Properties at the Interface between Two Flows
Comments
Boundary Layer in Non-Newtonian Flows
Symmetric Boundary Layer in Pseudo-Plastic Fluids
Weak Solutions of the Boundary Layer Continuation Problem for Pseudo-Plastic Fluids
Nonstationary Boundary Layer for Pseudo-Plastic Fluids
Continuation of the Boundary Layer in Dilatable Media
Symmetric Boundary Layer in Dilatable Media
Comments
Boundary Layer in Magnetic Hydrodynamics
Continuation of the MHD Boundary Layer in Ordinary Fluids
Solving the Equations of the MHD Boundary Layer in Pseudo-Plastic Fluids
Self-Similar Solutions of the MHD Boundary Layer System for a Dilatable Fluid
Solving the Equations of Boundary Layer for Dilatable Conducting Fluids in a Transversal Magnetic Field
Comments
Homogenization of Boundary Layer Equations
Homogenization of the Prandtl System with Rapidly Oscillating Injection and Suction
Homogenization of the Equations of the MHD Boundary Layer in a Rapidly Oscillating Magnetic Field
Comments
Some Open Problems
References
Index

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