Nonlinear Stability of Asymptotic Suction

Milan Miklavcic
Department of Mathematics
Michigan State University
East Lansing, MI 48824-1027

Published in AMS Transactions 281(1984), 215-231.
Also in IMA Preprint Series 5, 1982


Abstract:

Asymptotic suction velocity profile is an exact solution of the Navier-Stokes equations in halfspace.
The semigroup approach is used to show that evolution, determined by full Navier-Stokes equations, of initially small perturbations 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.

Here is the whole article in PDF format.

For my related publications see:

  1. Stability of mean flows over an infinite flat plate,
    Arch. Rational Mech. Anal. 80 (1982), 57-69.
    This is a joint work with M. Williams.

  2. Eigenvalues of the Orr-Sommerfeld equation in an unbounded domain,
    Arch. Rational Mech. Anal. 83(1983), 221-228.

  3. Eigenvalues of the Orr-Sommerfeld Equation
    Differential and Integral Equations, 4(1991), 731-737.

  4. Stability for semilinear parabolic equations with noninvertible linear operator (PDF file),
    Pacific J. Math. 118(1) (1985), 199-214.
    Also in IMA Preprint Series 22, 1983.

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