2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66432We 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}.arxiv version is already officialAnalysis of PDEstext