Wednesday, June 5, 2013

1306.0470 (Y. Charles Li)

The distinction of turbulence from chaos -- rough dependence on initial

Y. Charles Li
I believe that when the Reynolds number is large, violent fully developed turbulence is due to "rough dependence on initial data" rather than chaos which is caused by "sensitive dependence on initial data"; when the Reynolds number is moderate, (often transient) turbulence is due to chaos. In the current note, I derive an upper bound on the norm of the derivative of the solution map of the Navier-Stokes equations, as a first step toward understanding rough dependence on initial data.
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