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Long-time behavior of Navier-Stokes flow on a two-dimensional torus excited by an external sinusoidal force (1997)

Chen, Zhi-Min ; Price, W. G.

Springer

Journal of statistical physics 86 (1997), S. 301-335

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ISSN: 1572-9613

Keywords: Navier-Stokes equations ; bifurcations ; dynamical systems

Source: Springer Online Journal Archives 1860-2000

Topics: Physics

Notes: Abstract In this paper we study the Navier-Stokes flow on the two-dimensional torusS 1 ×S 1 excited by the external force (k 2 sinky, 0) and find the long-time behavior for the flow starting from some states, whereS 1=[0,2π](mod 2π). Especially for the casek=2, it follows from an analysis and computation that the Navier-Stokes flow with the initial state cos(mx+ny) or sin(mx+ny) will likely evolve through at most one step bifurcation to either a steady-state solution or a time-dependent periodic solution for any Reynolds number and integersm andn.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02180208

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