Dynamics Near the Subcritical Transition of the 3d Couette Flow: Below Threshold Case (Memoirs of the American Mathematical Society)

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Dynamics Near the Subcritical Transition of the 3d Couette Flow: Below Threshold Case (Memoirs of the American Mathematical Society) image
ISBN-10:

1470442175

ISBN-13:

9781470442170

Released: Oct 01, 2020
Format: Paperback, 154 pages

Description:

The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $\epsilon \leq c_0\mathbf {{Re}}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t \rightarrow \infty $. For times $t \gtrsim \mathbf {{Re}}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of ""2.5 dimensional'' streamwise-independent solutions referred to as streaks.

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