New Directions in Mathematical Fluid Mechanics

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

3. Homogenization of the Poisson—Boltzmann Equation

   • Youcef Amirat, Vladimir Shelukhin

   Pages 23-40

4. Superconducting Vortices: Chapman Full Model

   • S. N. Antontsev, N. V. Chemetov

   Pages 41-55

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

6. Oscillatory Limits with Changing Eigenvalues: A Formal Study

   • Didier Bresch, Benoît Desjardins, Emmanuel Grenier

   Pages 91-104

7. Finite-dimensional Control for the Navier—Stokes Equations

   • Alexander Yu. Chebotarev

   Pages 105-111

8. On the Sharp Vanishing Viscosity Limit of Viscous Incompressible Fluid Flows

   • H. Beirão da Veiga

   Pages 113-122

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

10. New Perspectives in Fluid Dynamics: Mathematical Analysis of a Model Proposed by Howard Brenner

    • Eduard Feireisl, Alexis Vasseur

    Pages 153-179

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

12. Optimal Neumann Control for the Two-dimensional Steady-state Navier-Stokes equations

    • A. V. Fursikov, R. Rannacher

    Pages 193-221

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

14. Unilateral Contact Problems Between an Elastic Plate and a Beam

    • Alexander Khludnev

    Pages 237-246

15. On Lighthill’s Acoustic Analogy for Low Mach Number Flows

    • William Layton, Antonín Novotný

    Pages 247-279

16. On the Uniqueness of Solutions to Boundary Value Problems for Non-stationary Euler Equations

    • Alexander E. Mamontov

    Pages 281-299

17. On Nonlinear Stability of MHD Equilibrium Figures

    • M. Padula

    Pages 301-331

18. Viscous Flows in Domains with a Multiply Connected Boundary

    • V. V. Pukhnachev

    Pages 333-348

19. Problems with Insufficient Information about Initial-boundary Data

    • E. V. Radkevich

    Pages 349-378

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

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.

• Boundary Control Problems
• Euler Equations
• Lagrangian Method
• Mathematical physics
• Navier-Stokes equation
• Navier–Stokes equation
• Non-equilibrium processes
• Poisson–Boltzmann Equation
• Stability problems
• convection
• fluid dynamics
• fluid mechanics
• fluid- and aerodynamics

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)

• 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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