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Ladyzhenskaya O.A. Mathematical Theory of Viscous Incompressible Flow

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Ladyzhenskaya O.A. Mathematical Theory of Viscous Incompressible Flow
2 ed. — Gordon and Breach, Science Publishers. Inc., 1969. — 234 p.
Contents.
Introduction.
Preliminaries.
Some Function Spaces and Inequalities.
The Vector Space L2(ti) and its Decomposition into Orthogonal Subspaces.
Riesz' Theorem and the Leray-Schauder Principle.
The Linearized Stationary Problem.
The Case of a Bounded Domain in E.
The Exterior Three-Dimensional Problem.
Plane-Parallel Flows.
The Spectrum of Linear Problems.
The Positivity of the Pressure.
The Theory of Hydrodynamical Potentials.
The Volume Potential.
Potentials of Single and Double Layers.
Investigation of the Integral Equations.
Green's Function.
Investigation of Solutions in Wr.
The Linear Nonstationary Problem.
Statement of the Problem. Existence and Uniqueness Theorems.
Investigation of the Differentiability Properties of Generalized Solutions.
Unbounded Domains and Behavior of Solutions as t^ + oo.
Expansion in Fourier Series.
The Vanishing Viscosity.
The Cauchy Problem.
The Nonlinear Stationary Problem.
The Case of Homogeneous Boundary Conditions.
The Interior Problem with Nonhomogeneous Boundary Conditions.
Flows in an Unbounded Domain.
Effective Estimates of Solutions.
The Differentiability Properties of Generalized Solutions.
The Behavior of Solutions as | x | -» + oo.
The Nonlinear Nonstationary Problem.
Statement of the Problem. The Uniqueness Theorem.
A Priori Estimates.
Existence Theorems.
Differentiability Properties of Generalized Solutions.
The Continuous Dependence of the Solutions on the Data of the Problem, and Their Behavior as.
Other Generalized Solutions of the Problem A).
Unbounded Domains and Vanishing Viscosity.
The Cauchy Problem.
Supplement I—New Equations for the Description of the Motion of Viscous.
ncompressible Fluids.
Comments.
Additional Comments.
References.
Name Index.
Subject Index.
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