Electron. J. Diff. Eqns., Vol. 2002(2002), No. 92, pp. 1-15.

Resolvent estimates for 2-dimensional perturbations of plane Couette flow

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 $L_2$ 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.

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
e-mail: pablo@math.unm.edu

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