Hydrodynamic Stability at High Reynolds Number and Transition Threshold Problem
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Overview
Syllabus
Intro
Reynolds experiment in 1883
Mathematical model Navier-Stokes equations
Examples of laminar flow
Eigenvalue analysis
Subcritical transition
Transition threshold problem
Numerics and asymptotic analysis results
Mathematical analysis results
Key factors influencing the threshold
Linear inviscid damping: monotone flow
Linear inviscid damping: Kolmogorov flow
Linear inviscid damping: methods of the proof The key ingredient of the proof is to solve the inhomogeneous
Nonlinear inviscid damping
Linear enhanced dissipation
Chapman toy model Consider a toy model introduced by Chapman
Chapman tay model: scaling analysis
Chapman tay model: secondary instability
Chapman toy model: transition route
Perturbation NS system
Secondary instability of wall mode
Transition threshold for 3-D Couette flow
Key ingredients(l): space-time estimates
Key ingredients (ll): exclude secondary instability
Key ingredients(lll): energy functional
Open problems
Taught by
International Mathematical Union