Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)2022-03-142022-03-14https://noesis.uis.edu.co/handle/20.500.14071/7092In this expository article, we discuss the application of the resolvent technique to prove nonlinear stability of 2 dimensional plane Couette flow. Using this technique, we show how one can derive a threshold amplitude for perturbations that can lead to turbulence in terms of the parameter called Reynolds number. Our objective is to present this argument in details, trying to be accessible to a wide class of readers, and hopefully catching their attention to the beautiful subject of stability questions in fluid mechanics.   application/pdfCouette flowresolvent estimatesnonlinear stabilityinfo:eu-repo/semantics/articlehttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)