Abstract.
We derive a sufficient condition for stability of a steady solution of the Navier–Stokes equation in a 3D exterior domain Ω. The condition is formulated as a requirement on integrability on the time interval (0, +∞) of a semigroup generated by the linearized problem for perturbations, applied to a finite family of certain functions. The norm of the semigroup is measured in a bounded sub-domain of Ω. We do not use any condition on “smallness” of the basic steady solution.
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Communicated by G. P. Galdi
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Neustupa, J. Stability of a Steady Viscous Incompressible Flow Past an Obstacle. J. math. fluid mech. 11, 22–45 (2009). https://doi.org/10.1007/s00021-007-0246-x
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DOI: https://doi.org/10.1007/s00021-007-0246-x