An Introduction to the Mathematics of Hydrodynamic Stability at High Reynolds Number

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	Front matterDownload pp. i–iv
	Prefacepp. v–vi
	ContentsDownload pp. vii–ix
1	The incompressible Navier–Stokes and Euler equationspp. 3–12
2	An introduction to hydrodynamic stabilitypp. 13–19
3	Spectral vs. linear stabilitypp. 23–25
4	Basic considerations and case studiespp. 27–41
5	Inviscid problems: Rayleigh's equationpp. 43–50
6	Case study: Long wave instabilitiespp. 51–63
7	Case study: Sharp inviscid damping estimates for strictly monotone shear flows in $T \times R$ pp. 65–82
8	Viscous problems: The Orr–Sommerfeld equationpp. 83–93
9	Case study: Self-similar Oseen vortexpp. 95–97
10	Case study: Couette flow in a channelpp. 99–103
11	Case study: Boundary-driven instabilitiespp. 105–113
12	A brief survey of other linearized resultspp. 115–116
13	Variational methods for nonlinear stabilitypp. 119–126
14	Case study: Nonlinear inviscid damping for the 2D Couette flowpp. 127–145
15	Quantitative stability thresholdspp. 149–151
16	Case study: Stability thresholds for 2D Couette flowpp. 153–162
17	Case study: Subcritical transition in the 3D Couette flowpp. 163–176
18	A brief survey of other nonlinear (in)stability resultspp. 177–178
A	Fourier analysisp. 181
B	Sobolev spacespp. 183–185
C	Gevrey and analytic regularitypp. 187–188
D	Airy functionsp. 189
E	Theory of linear operatorspp. 191–195
	Referencespp. 197–208