Bounds for the threshold amplitude for plane Couette flow

Mattias Liefvendahl; Gunilla Kreiss

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Bounds for the threshold amplitude for plane Couette flow

Mattias Liefvendahl·Gunilla Kreiss

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Abstract

We prove nonlinear stability for finite amplitude perturbations of plane Couette flow. A bound of the solution of the resolvent equation in the unstable complex half-plane is used to estimate the solution of the full nonlinear problem.The result is a lower bound, including Reynolds number dependence,of the threshold amplitude below which all perturbations are stable. Our result is an improvement of the corresponding bound derived in \cite{KLH:1}.

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Mattias Liefvendahl, Gunilla Kreiss. 2003-02-03. Bounds for the threshold amplitude for plane Couette flow. https://arxiv.org/abs/math/0302028

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