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