The Navier-Stokes Equations Theory and Numerical Methods

1. Front Matter

   Pages I-VII

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2. Open problems in the theory of the Navier-Stokes equations for viscous incompressible flow

   • John G. Heywood

   Pages 1-22

3. Navier-Stokes equations from the point of view of the theory of ill-posed boundary value problems

   • A. V. Fursikov

   Pages 23-39

4. On the statistical approach to the Navier-Stokes equations

   • A. V. Fursikov

   Pages 40-48

5. Asymptotic expansions for a flow with a dynamic contact angle

   • Dietmar Kröner

   Pages 49-59

6. Noncompact free boundary problems for the Navier-Stokes equations

   • Konstantin Pileckas

   Pages 60-72

7. On large time behavior of the total kinetic energy for weak solutions of the Navier-Stokes equations in unbounded domains

   • Wolfgang Borchers, Tetsuro Miyakawa

   Pages 73-83

8. Strong solution for the Navier-Stokes flow in the half-space

   • Hideo Kozono

   Pages 84-86

9. The problem of momentumless flow for the Navier-Stokes equations

   • V. V. Pukhnachov

   Pages 87-94

10. Decay and stability in L _p for strong solutions of the Cauchyproblem for the Navier-Stokes equations

    • Michael Wiegner

    Pages 95-99

11. A Galerkin approximation for linear eigenvalue problems in two and three-dimensional boundary-layer flows

    • T. M. Fischer

    Pages 100-108

12. Symmetry-breaking effects of distant sidewalls in Rayleigh-Bénard convection

    • Wayne Nagata

    Pages 109-116

13. Applications of degenerate bifurcation equations to the taylor problem and the water wave problem

    • Hisashi Okamoto

    Pages 117-127

14. A uniqueness criterion for the solution of the stationary Navier-Stokes equations

    • Giovanni Prouse

    Pages 128-133

15. On decay properties of the Stokes equations in exterior domains

    • Hermann Sohr, Werner Varnhorn

    Pages 134-151

16. On necessary and sufficient conditions for the solvability of the equations rot μ=γ and div μ=ε with μ vanishing on the boundary

    • Wolf von Wahl

    Pages 152-157

17. On optimal constants in some inequalities

    • Waldemar Velte

    Pages 158-168

18. Boundary-value problems for Navier-Stokes equations of viscous gas

    • A. V. Kazhikhov

    Pages 169-172

19. On the one-dimensional Navier-Stokes equations for compressible fluids

    • Alberto Valli

    Pages 173-179

20. On the numerical analysis of the nonstationary Navier-Stokes equations

    • Rolf Rannacher

    Pages 180-193

These proceedings contain original (refereed) research articles by specialists from many countries, on a wide variety of aspects of Navier-Stokes equations. Additionally, 2 survey articles intended for a general readership are included: one surveys the present state of the subject via open problems, and the other deals with the interplay between theory and numerical analysis.

• Navier-Stokes equation
• convection
• finite element method
• numerical analysis
• stability

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