2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64739We present results concerning resolvent estimates for the linear operator associated with the system of differential equations governing perturbations of the Couette flow. We prove estimates on the L_2 norm of the resolvent of this operator showing this norm to be proportional to the Reynolds number R for a region of the unstable half plane. For the remaining region, we show that the problem can be reduced to estimating the solution of a homogeneous ordinary differential equation with non-homogeneous boundary conditions. Numerical approximations indicate that the norm of the resolvent is proportional to R in the whole region of interest.16 pages, 4 figures. A mistake in the proof of Theorem 1 was corrected. The presentation was changed a little, and typos were correctedAnalysis of PDEs76E05; 47A10text