Dynamics near the subcritical transition of the 3D Couette flow I : below threshold case

書誌事項

Dynamics near the subcritical transition of the 3D Couette flow I : below threshold case

Jacob Bedrossian, Pierre Germain, Nader Masmoudi

(Memoirs of the American Mathematical Society, no. 1294)

American Mathematical Society, c2020

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注記

"July 2020, volume 266, number 1294 (fourth of 6 numbers)"

Includes bibliographical reference (p. 155-158)

内容説明・目次

内容説明

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,ドル the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2,ドル and returns to the Couette flow as $t \rightarrow \infty $. For times $t \gtrsim \mathbf {Re}^1/3,ドル 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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