A Five-Dimensional System of Navier-Stokes Equation for a Two-Dimensional Incompressible Fluid on a Torus
Year: 2016
Author: Heyuan Wang, Kaitai Li
Journal of Partial Differential Equations, Vol. 29 (2016), Iss. 4 : pp. 255–268
Abstract
A five-mode truncation of Navier-Stokes equation for a two-dimensional incompressible fluid on a torus is studied. Its stationary solutions and stability are presented, the existence of attractor and the global stability of the system are discussed. The whole process, which shows a chaos behavior approached through an involved sequence of bifurcations with the changing of Reynolds number, is simulated numerically. Based on numerical simulation results of bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system are revealed.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v29.n4.1
Journal of Partial Differential Equations, Vol. 29 (2016), Iss. 4 : pp. 255–268
Published online: 2016-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Navier-Stokes equation