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

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 glob...

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Bibliographic Details
Main Authors: Bedrossian, Jacob, Germain, Pierre, Masmoudi, Nader
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2020
Series:Memoirs of the American Mathematical Society
Subjects:
Damping (Mechanics)
Inviscid flow
Mixing
Shear flow
Stability
Three-dimensional modeling
Viscous flow
Viscous flow > Mathematical models
ISBN:1470442175, 9781470442170
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Table of Contents:
  • Introduction -- Outline of the proof -- Regularization and continuation -- High norm estimate on <inline-formula content-type="math/mathml"> Q 2 Q^2 </inline-formula> -- High norm estimate on <inline-formula content-type="math/mathml"> Q 3 Q^3 </inline-formula> -- High norm estimate on <inline-formula content-type="math/mathml"> Q 0 1 Q^1_0 </inline-formula> -- High norm estimate on <inline-formula content-type="math/mathml"> Q ≠<!-- ≠ --> 1 Q^1_{\neq } </inline-formula> -- Coordinate system controls -- Enhanced dissipation estimates -- Sobolev estimates -- Acknowledgments -- Fourier analysis conventions, elementary inequalities, and Gevrey spaces -- Definition and analysis of norms -- Multiplier and paraproduct tools -- Elliptic estimates