Hydrodynamic Stability at High Reynolds Number and Transition Threshold Problem

Hydrodynamic Stability at High Reynolds Number and Transition Threshold Problem

International Mathematical Union via YouTube Direct link

Intro

1 of 26

1 of 26

Intro

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Hydrodynamic Stability at High Reynolds Number and Transition Threshold Problem

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  1. 1 Intro
  2. 2 Reynolds experiment in 1883
  3. 3 Mathematical model Navier-Stokes equations
  4. 4 Examples of laminar flow
  5. 5 Eigenvalue analysis
  6. 6 Subcritical transition
  7. 7 Transition threshold problem
  8. 8 Numerics and asymptotic analysis results
  9. 9 Mathematical analysis results
  10. 10 Key factors influencing the threshold
  11. 11 Linear inviscid damping: monotone flow
  12. 12 Linear inviscid damping: Kolmogorov flow
  13. 13 Linear inviscid damping: methods of the proof The key ingredient of the proof is to solve the inhomogeneous
  14. 14 Nonlinear inviscid damping
  15. 15 Linear enhanced dissipation
  16. 16 Chapman toy model Consider a toy model introduced by Chapman
  17. 17 Chapman tay model: scaling analysis
  18. 18 Chapman tay model: secondary instability
  19. 19 Chapman toy model: transition route
  20. 20 Perturbation NS system
  21. 21 Secondary instability of wall mode
  22. 22 Transition threshold for 3-D Couette flow
  23. 23 Key ingredients(l): space-time estimates
  24. 24 Key ingredients (ll): exclude secondary instability
  25. 25 Key ingredients(lll): energy functional
  26. 26 Open problems

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