Resolvent Estimates for 2-Dimensional Perturbations of Plane Couette Flow
Files
Date
2002-10-27
Authors
Braz e Silva, Pablo
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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 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.
Description
Keywords
Couette flow, Resolvent estimates
Citation
Braz e Silva, P. (2002). Resolvent estimates for 2-dimensional perturbations of plane Couette flow. <i>Electronic Journal of Differential Equations, 2002</i>(92), pp. 1-15.
Rights
Attribution 4.0 International