Dynamics Near the Subcritical Transition of the 3D Couette Flow I(English, Paperback, Bedrossian Jacob)

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Dynamics Near the Subcritical Transition of the 3D Couette Flow I(English, Paperback, Bedrossian Jacob) is written by Bedrossian Jacob and published by American Mathematical Society. It's available with International Standard Book Number or ISBN identification 1470442175 (ISBN 10) and 9781470442170 (ISBN 13).

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.