Nonlinear stability of asymptotic suction

Miklavčič, Milan

doi:10.1090/S0002-9947-1984-0719667-9

Nonlinear stability of asymptotic suction
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Trans. Amer. Math. Soc. 281 (1984), 215-231 Request permission

Abstract:

The semigroup approach to the Navier-Stokes equation in halfspace is used to prove that the stability of the asymptotic suction velocity profile is determined by the eigenvalues of the classical Orr-Sommerfeld equation. The usual obstacle, namely, that the corresponding linear operator contains $0$ in the spectrum is removed with the use of weighted spaces.

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