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Resolvent estimates for 2 dimensional perturbations of plane Couette Flow

Pablo Braz e Silva
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Abstract

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 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.

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Pablo Braz e Silva. 2002-09-24. Resolvent estimates for 2 dimensional perturbations of plane Couette Flow. https://arxiv.org/abs/math/0208139

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