2002/08/31 by Pablo Braz e Silva
Mathematics · #math.AP #msc:76E05 #msc:47A10
published as Electron. J. Diff. Eqns., Vol. 2002(2002), No. 92, pp. 1-15 · 16 pages, 4 figures. A mistake in the proof of Theorem 1 was corrected. The presentation was changed a little, and typos were corrected
arxiv created 2002/09/24 · arxiv updated 2009/11/30
We 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 L2 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.