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On the stability of boundary layers of incompressible Euler equations. (English) Zbl 0958.35106
The author studies the stability of the boundary layer of 2D-incompressible Euler equations in a periodic half strip. Using energy methods, he shows under certain assumptions (which roughly speaking say that there is no inflection point in the boundary layer profile) the linear stability of the Euler equations and, under some additional assumptions, he also proves the nonlinear stability. As an application, the asymptotic expansion of the boundary layer is proved.
The other part deals with instability results; using the result of Lord Rayleigh [On the stability, or instability of certain fluid motions, Proc. London Math. Soc. 11, 57-70 (1880)], where the linear instability is shown, the author constructs an example where the solution to the nonlinear system is unstable. Indeed, in this case there is an inflection point in the boundary layer profile.

35Q35 PDEs in connection with fluid mechanics
35Q05 Euler-Poisson-Darboux equations
76E17 Interfacial stability and instability in hydrodynamic stability
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
Full Text: DOI
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