A computer-assisted analysis of the two dimensional Navier-Stokes equations

  • H. Okamoto
  • M. Shōji
  • M. Katsurada
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1540)


Complicated behaviour is common in solutions to the Navier-Stokes equations when the viscosity is small. The mechanism of the complexities is obscure even today. Here is a reason why numerical computations play an important role in making a qualitative picture of the Navier-Stokes flows. The purpose of this paper is to explain, through examples, necessity of numerical computations in the analysis of the Navier-Stokes equations. More specifically, we consider two dimensional freely decaying flow and the Kolmogorov problem.


Reynolds Number Euler Equation Bifurcation Diagram Basic Solution Dynamical System Theory 
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Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • H. Okamoto
    • 1
  • M. Shōji
    • 2
  • M. Katsurada
    • 3
  1. 1.Research Institute for Mathematical SciencesKyoto UniversityKyotoJapan
  2. 2.Department of Mathematical SciencesUniversity of TokyoTokyoJapan
  3. 3.Department of MathematicsMeiji UniversityKawasakiJapan

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