Limiting Behavior for an Iterated Viscosity
Department of Mathematics, Indiana University,
Bloomington, IN, 47405, USA. (firstname.lastname@example.org)
2 Gaithersburg, MD, 20878, USA.
The behavior of an ordinary differential equation for the low wave number velocity mode is analyzed. This equation was derived in  by an iterative process on the two-dimensional Navier-Stokes equations (NSE). It resembles the NSE in form, except that the kinematic viscosity is replaced by an iterated viscosity which is a partial sum, dependent on the low-mode velocity. The convergence of this sum as the number of iterations is taken to be arbitrarily large is explored. This leads to a limiting dynamical system which displays several unusual mathematical features.
Mathematics Subject Classification: 35Q30 / 37L65
Key words: Navier-Stokes.
© EDP Sciences, SMAI, 2000