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New Directions in Mathematical Fluid Mechanics

The Alexander V. Kazhikhov Memorial Volume

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  • © 2010
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Overview

Editors:
  1. Andrei V. Fursikov

    1. Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia

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  2. Giovanni P. Galdi

    1. Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, USA

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  3. Vladislav V. Pukhnachev

    1. Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russia

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  • Contributions by leading experts in the field of mathematical physics and mathematical fluid mechanics
  • The state of the art of a broad range of topics is presented
  • Dedicated to the memory of A.V. Kazhikhov
  • Includes supplementary material: sn.pub/extras

Part of the book series: Advances in Mathematical Fluid Mechanics (AMFM)

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Table of contents (20 chapters)

  1. Front Matter

    Pages i-xi
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  2. Boundary Control Problems for Stationary Equations of Heat Convection

    • G. V. Alekseev, D. A. Tereshko
    Pages 1-21
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  3. Homogenization of the Poisson—Boltzmann Equation

    • Youcef Amirat, Vladimir Shelukhin
    Pages 23-40
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  4. Superconducting Vortices: Chapman Full Model

    • S. N. Antontsev, N. V. Chemetov
    Pages 41-55
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  5. Augmented Lagrangian Method and Compressible Visco-plastic Flows: Applications to Shallow Dense Avalanches

    • D. Bresch, E. D. Fernández-Nieto, I. R. Ionescu, P. Vigneaux
    Pages 57-89
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  6. Oscillatory Limits with Changing Eigenvalues: A Formal Study

    • Didier Bresch, Benoît Desjardins, Emmanuel Grenier
    Pages 91-104
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  7. Finite-dimensional Control for the Navier—Stokes Equations

    • Alexander Yu. Chebotarev
    Pages 105-111
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  8. On the Sharp Vanishing Viscosity Limit of Viscous Incompressible Fluid Flows

    • H. Beirão da Veiga
    Pages 113-122
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  9. Small Péclet Number Approximation as a Singular Limit of the Full Navier-Stokes-Fourier System with Radiation

    • Eduard Feireisl, Antonín Novotný
    Pages 123-152
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  10. New Perspectives in Fluid Dynamics: Mathematical Analysis of a Model Proposed by Howard Brenner

    • Eduard Feireisl, Alexis Vasseur
    Pages 153-179
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  11. Existence of a Regular Periodic Solution to the Rothe Approximation of the Navier—Stokes Equation in Arbitrary Dimension

    • Jens Frehse, Michael Růžička
    Pages 181-192
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  12. Optimal Neumann Control for the Two-dimensional Steady-state Navier-Stokes equations

    • A. V. Fursikov, R. Rannacher
    Pages 193-221
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  13. On Some Boundary Value Problem for the Stokes Equations with a Parameter in an Infinite Sector

    • Shigeharu Itoh, Naoto Tanaka, Atusi Tani
    Pages 223-236
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  14. Unilateral Contact Problems Between an Elastic Plate and a Beam

    • Alexander Khludnev
    Pages 237-246
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  15. On Lighthill’s Acoustic Analogy for Low Mach Number Flows

    • William Layton, Antonín Novotný
    Pages 247-279
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  16. On the Uniqueness of Solutions to Boundary Value Problems for Non-stationary Euler Equations

    • Alexander E. Mamontov
    Pages 281-299
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  17. On Nonlinear Stability of MHD Equilibrium Figures

    • M. Padula
    Pages 301-331
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  18. Viscous Flows in Domains with a Multiply Connected Boundary

    • V. V. Pukhnachev
    Pages 333-348
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  19. Problems with Insufficient Information about Initial-boundary Data

    • E. V. Radkevich
    Pages 349-378
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  20. On the Stability of Non-symmetric Equilibrium Figures of Rotating Self-gravitating Liquid not Subjected to Capillary Forces

    • V. A. Solonnikov
    Pages 379-414
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Keywords

About this book

On November 3, 2005, Alexander Vasil’evich Kazhikhov left this world, untimely and unexpectedly. He was one of the most in?uential mathematicians in the mechanics of ?uids, and will be remembered for his outstanding results that had, and still have, a c- siderablysigni?cantin?uenceinthe?eld.Amonghis manyachievements,werecall that he was the founder of the modern mathematical theory of the Navier-Stokes equations describing one- and two-dimensional motions of a viscous, compressible and heat-conducting gas. A brief account of Professor Kazhikhov’s contributions to science is provided in the following article “Scienti?c portrait of Alexander Vasil’evich Kazhikhov”. This volume is meant to be an expression of high regard to his memory, from most of his friends and his colleagues. In particular, it collects a selection of papers that represent the latest progress in a number of new important directions of Mathematical Physics, mainly of Mathematical Fluid Mechanics. These papers are written by world renowned specialists. Most of them were friends, students or colleagues of Professor Kazhikhov, who either worked with him directly, or met him many times in o?cial scienti?c meetings, where they had the opportunity of discussing problems of common interest.

Reviews

From the reviews:

“The book … is a collection of papers that represent the latest progress in a number of new important directions of Mathematical Physics, mainly of Mathematical Fluid Mechanics. … The volume could be helpful to specialists as well as to researchers who would like to become acquainted with certain aspects of Mathematical Fluid Mechanics, and may also serve as a stimulating starting point for further research.” (Ciprian Deliu, IASI Polytechnic Magazine, Vol. 22 (1/4), March-December, 2010)

Editors and Affiliations

  • Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia

    Andrei V. Fursikov

  • Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, USA

    Giovanni P. Galdi

  • Lavrentyev Institute of Hydrodynamics, Novosibirsk, Russia

    Vladislav V. Pukhnachev

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