Mathematical Fluid Mechanics

1. Front Matter

   Pages i-ix

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2. What Use for the Mathematical Theory of the Navier-Stokes Equations

   • Claude Bardos

   Pages 1-25

3. An Iterative Scheme for Steady Compressible Viscous Flow, Modified to Treat Large Potential Forces

   • Markus Bause, John G. Heywood, Antonín Novotný, Mariarosaria Padula

   Pages 27-45

4. Asymptotic Results for the Linear Stage of the Rayleigh—Taylor Instability

   • Catherine Cherfils—Clérouin, Olivier Lafitte, Pierre-Arnaud Raviart

   Pages 47-71

5. Recent Progress in the Mathematical Theory of Viscous Compressible Fluids

   • Eduard Feireisl

   Pages 73-103

6. Numerical Methods for Compressible Flow

   • Miloslav Feistauer

   Pages 105-142

7. Instability of Steady Flows of an Ideal Incompressible Fluid

   • Susan Friedlander, Alexander Shnirelman

   Pages 143-172

8. Finite Volume Solution of 2D and 3D Euler and Navier-Stokes Equations

   • J. Fürst, M. Janda, K. Kozel

   Pages 173-193

9. On a Conjecture Concerning the Stokes Problem in Nonsmooth Domains

   • John G. Heywood

   Pages 195-205

10. On Well—Posedness of the Navier—Stokes Equations

    • Hideo Kozono

    Pages 207-236

11. Anisotropic and Geometric Criteria for Interior Regularity of Weak Solutions to the 3D Navier—Stokes Equations

    • Jiří Neustupa, Patrick Penel

    Pages 237-265

12. Back Matter

    Pages 267-269

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Mathematical modeling and numerical simulation in fluid mechanics are topics of great importance both in theory and technical applications. The present book attempts to describe the current status in various areas of research. The 10 chapters, mostly survey articles, are written by internationally renowned specialists and offer a range of approaches to and views of the essential questions and problems. In particular, the theories of incompressible and compressible Navier-Stokes equations are considered, as well as stability theory and numerical methods in fluid mechanics. Although the book is primarily written for researchers in the field, it will also serve as a valuable source of information to graduate students.

• Navier-Stokes equation
• Potential
• fluid mechanics
• functional analysis
• mathematical modeling
• partial differential equation
• partial differential equations
• simulation
• stability

• Department of Technical Mathematics, Faculty of Mechanical Engineering, Czech Technical University, Praha 2, Czech Republic

  Jiří Neustupa

• Département de Mathématiques, Université de Toulon et du Var, La Garde Cedex, France

  Patrick Penel

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