Pablo Braz e Silva
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.
Submitted September 24, 2002. Published October 27, 2002.
Math Subject Classifications: 76E05, 47A10.
Key Words: Couette flow, resolvent estimates.
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|Pablo Braz e Silva |
The University of New Mexico
Department of Mathematics and Statistics
Albuquerque, NM 87131, USA
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