Volume 29, Issue 4
A Five-Dimensional System of Navier-Stokes Equation for a Two-Dimensional Incompressible Fluid on a Torus

Heyuan WangKaitai Li

J. Part. Diff. Eq., 29 (2016), pp. 255-268.

Published online: 2016-12

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  • 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.

  • Keywords

Navier-Stokes equation strange attractor Lyapunov function bifurcation chaos

  • AMS Subject Headings

65N30, 47H15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

wangheyuan6400@sina.com (Heyuan Wang)

ktli@xitu.edu.cn (Kaitai Li)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-29-255, author = {Wang , Heyuan and Li , Kaitai}, title = {A Five-Dimensional System of Navier-Stokes Equation for a Two-Dimensional Incompressible Fluid on a Torus}, journal = {Journal of Partial Differential Equations}, year = {2016}, volume = {29}, number = {4}, pages = {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.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v29.n4.1}, url = {http://global-sci.org/intro/article_detail/jpde/5092.html} }
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.
Heyuan Wang & Kaitai Li. (2019). A Five-Dimensional System of Navier-Stokes Equation for a Two-Dimensional Incompressible Fluid on a Torus. Journal of Partial Differential Equations. 29 (4). 255-268. doi:10.4208/jpde.v29.n4.1
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