Bounds for the threshold amplitude for plane couette flow

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 [3]. © 2002 Taylor & Francis Group, LLC.