Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case

Released on by Jacob Bedrossian
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  • Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case Book Detail

  • Author : Jacob Bedrossian
  • Release Date : 2020-09-28
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 154
  • ISBN 13 : 1470442175
  • File Size : 44,44 MB
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Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case by Jacob Bedrossian PDF Summary

Book 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 $epsilon leq c_0mathbf {Re}^-1$ 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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