Nonlinear stability of asymptotic suction

Miklavčič, Milan

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

Nonlinear stability of asymptotic suction
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by Milan Miklavčič

Trans. Amer. Math. Soc. 281 (1984), 215-231

DOI: https://doi.org/10.1090/S0002-9947-1984-0719667-9

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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.

References

P. G. Drazin and William Hill Reid, Hydrodynamic stability, Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, Cambridge-New York, 1981. MR 604359
Hiroshi Fujita and Tosio Kato, On the Navier-Stokes initial value problem. I, Arch. Rational Mech. Anal. 16 (1964), 269–315. MR 166499, DOI 10.1007/BF00276188
Giovanni P. Galdi, Variational methods for stability of fluid motions in unbounded domains, Ricerche Mat. 27 (1978), no. 2, 387–404. MR 527429
Giovanni P. Galdi and Salvatore Rionero, On magnetohydrodynamic motions in unbounded domains: stability and uniqueness, Ann. Mat. Pura Appl. (4) 115 (1977), 119–154 (1978). MR 475228, DOI 10.1007/BF02414713
G. P. Galdi and S. Rionero, Local estimates and stability of viscous flows in an exterior domain, Arch. Rational Mech. Anal. 81 (1983), no. 4, 333–347. MR 683194, DOI 10.1007/BF00250859

A universal stability criterion in unbounded domains

Daniel Henry, Geometric theory of semilinear parabolic equations, Lecture Notes in Mathematics, vol. 840, Springer-Verlag, Berlin-New York, 1981. MR 610244, DOI 10.1007/BFb0089647
Daniel D. Joseph, Stability of fluid motions. I, Springer Tracts in Natural Philosophy, Vol. 27, Springer-Verlag, Berlin-New York, 1976. MR 0449147

Perturbation theory for linear operators

Milan Miklavčič, Eigenvalues of the Orr-Sommerfeld equation in an unbounded domain, Arch. Rational Mech. Anal. 83 (1983), no. 3, 221–228. MR 701903, DOI 10.1007/BF00251509
Milan Miklavčič and Michael Williams, Stability of mean flows over an infinite flat plate, Arch. Rational Mech. Anal. 80 (1982), no. 1, 57–69. MR 656802, DOI 10.1007/BF00251524
Hermann Schlichting, Boundary layer theory, McGraw-Hill, New York; Pergamon Press, London; Verlag G. Braun, Karlsruhe, 1955. Translated by J. Kestin. MR 0076530
James Serrin, On the stability of viscous fluid motions, Arch. Rational Mech. Anal. 3 (1959), 1–13. MR 105250, DOI 10.1007/BF00284160