A computer-assisted analysis of the two dimensional Navier-Stokes equations
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.
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- 5.M. Katsurada, H. Okamoto, and M. Shōji, Bifurcation of the stationary Navier-Stokes flows on a 2-D flat torus, to appear in Proc. Katata workshop on “Nonlinear PDEs and Applications”, eds. T. Nishida and M. Mimura.Google Scholar
- 6.H.B. Keller, “Lectures on Numerical Methods in Bifurcation Theory (Tata Institute of Fundamental Research No. 79),” Springer Verlag, 1987.Google Scholar
- 7.S. Kida and M. Yamada, Singularity and energy spectrum in a two dimensional incompressible inviscid flow, in “Turbulence and Chaotic Phenomena in Fluids”, ed. T. Tatsumi, North-Holland, Proc. IUTAM Symposium in 1984.Google Scholar
- 8.A. Majda, Vorticity and the mathematical theory of incompressible fluid flow, Comm. Pure Appl. Math. 39 (1986).Google Scholar
- 9.H. Okamoto, and M. Shōji, Bifurcation diagrams in Kolmogorov's problem of viscous incompressible fluid on 2-D flat tori., submitted.Google Scholar