Overview

The main topics in this volume reflect the fields of mathematics in which Professor O.A. Ladyzhenskaya obtained her most influential results. One of the main topics considered in the volume is the Navier-Stokes equations. This subject is investigated in many different directions. In particular, the existence and uniqueness results are obtained for the Navier-Stokes equations in spaces of low regularity. A sufficient condition for the regularity of solutions to the evolution Navier-Stokes equations in the three-dimensional case is derived and the stabilization of a solution to the Navier-Stokes equations to the steady-state solution and the realization of stabilization by a feedback boundary control are discussed in detail. Connections between the regularity problem for the Navier-Stokes equations and a backward uniqueness problem for the heat operator are also clarified.

Full Product Details

Author:   Michael Sh. Birman ,  Stefan Hildebrandt ,  Vsevolod A. Solonnikov ,  Nina N. Uraltseva
Publisher:   Springer Science+Business Media
Imprint:   Kluwer Academic/Plenum Publishers
Edition:   2002 ed.
Volume:   2
Dimensions:   Width: 15.50cm , Height: 2.50cm , Length: 23.50cm
Weight:   1.650kg
ISBN:  

9780306474224

ISBN 10:   0306474220
Pages:   380
Publication Date:   31 January 2003
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Nonhomogeneous Navier-Stokes Equations with Integrable Low-Regularity Data.- On the Rectifiability of Defect Measures Arising in a Micromagnetics Model.- Vorticity and Smoothness in Viscous Flows.- Absolute Continuity of the Spectrum of the Periodic Operator of Elasticity Theory for Constant Shear Modulus.- Some Properties of Solutions of Fully Nonlinear Partial Differential Inequalities.- On Time-Discretizations for Generalized Newtonian Fluids.- A Stokes-Like System for Mixtures.- Real Processes and Realizability of a Stabilization Method for the Navier-Stokes Equations by Boundary Feedback Control.- On the Inelastic Boltzmann Equation with Diffusive Forcing.- On Correct Mathematical Description of Processes in Continuous Media with Maxwell Viscosity.- Uniqueness of Recovery of Some Systems of Quasilinear Elliptic and Parabolic Partial Differential Equations.- Global Solution of Coupled Kuramoto-Sivashinsky and Ginzburg-Landau Equations.- On Skyrme’s Model.- Linear and Nonlinear Ultraparabolic Equations of Kolmogorov Type Arising in Diffusion Theory and in Finance.- On the Dimension of the Global Attractor for the Modified Navier Stokes Equations.- The Diffusion Velocity Method as a Tool for General Diffusion Equations.- Harnack Inequalities on Scale Irregular Sierpinski Gaskets.- Mean Value Theorems and Harnack Inequalities for Second-Order Parabolic Equations.- The Navier-Stokes Equations and Backward Uniqueness.- Hessian Equations on Compact Riemannian Manifolds.

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