TY - JOUR
T1 - A Five-Dimensional System of Navier-Stokes Equation for a Two-Dimensional Incompressible Fluid on a Torus
AU - Wang , Heyuan
AU - Li , Kaitai
JO - Journal of Partial Differential Equations
VL - 4
SP - 255
EP - 268
PY - 2016
DA - 2016/12
SN - 29
DO - http://doi.org/10.4208/jpde.v29.n4.1
UR - https://global-sci.org/intro/article_detail/jpde/5092.html
KW - Navier-Stokes equation
KW - strange attractor
KW - Lyapunov function
KW - bifurcation
KW - chaos
AB -  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.