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Limiting behavior for an iterated viscosity. (English) Zbl 0962.76022

Summary: We analyze the behavior of an ordinary differential equation for the low wave number velocity mode. This equation was derived by an iterative process applied to the two-dimensional Navier-Stokes equations. It resembles the Navier-Stokes equations in form, except that the kinematic viscosity is replaced by an iterated viscosity which is a partial sum, dependent on the low-mode velocity. We explore the convergence of this sum as the number of iterations is arbitrarily large. This leads to a limiting dynamical system which displays several unusual mathematical features.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
37N10 Dynamical systems in fluid mechanics, oceanography and meteorology
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References:

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