Mathematical Models in Boundary Layer Theory

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