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

About the Author Jacob Bedrossian, University of Maryland, College Park, MD, Pierre Germain, Courant Institute of Mathematical Sciences, New York, NY Nader Masmoudi, Courant Institute of Mathematical Sciences, New York City, NY Product 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.