Geodesic
Resolvent estimates for 2-dimensional perturbations of plane Couette flow
Electronic journal of differential equations, Tome 2002 (2002)
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.
Classification : 76E05, 47A10
Keywords: Couette flow, resolvent estimates 
@article{EJDE_2002__2002__a232,
     author = {Braz e Silva,  Pablo},
     title = {Resolvent estimates for 2-dimensional perturbations of plane {Couette} flow},
     journal = {Electronic journal of differential equations},
     year = {2002},
     volume = {2002},
     zbl = {1035.76014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a232/}
}
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JO  - Electronic journal of differential equations
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%0 Journal Article
%A Braz e Silva,  Pablo
%T Resolvent estimates for 2-dimensional perturbations of plane Couette flow
%J Electronic journal of differential equations
%D 2002
%V 2002
%U http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a232/
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%F EJDE_2002__2002__a232
Braz e Silva,  Pablo. Resolvent estimates for 2-dimensional perturbations of plane Couette flow. Electronic journal of differential equations, Tome 2002 (2002). http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a232/