Electron. J. Diff. Eqns., Vol. 2002(2002), No. 92, pp. 115.
Resolvent estimates for 2dimensional perturbations
of plane Couette flow
Pablo Braz e Silva
Abstract:
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 nonhomogeneous 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
email: pablo@math.unm.edu

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