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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)

Abstract

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.

Keywords

Reynolds Number Euler Equation Bifurcation Diagram Basic Solution Dynamical System Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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