We present results concerning resolvent estimates for the linear operator associated with the system of differential equations governing 2 dimensional perturbations of plane Couette flow. We prove estimates on the
norm of the resolvent of this
operator showing this norm to be proportional to the Reynolds
number
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
in the whole region of interest.
