Geodesic
Resolvent estimates for 2-dimensional perturbations of plane Couette flow
Electronic Journal of Differential Equations, Tome 2002 (2002).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a132,
     author = {Braz e Silva, Pablo},
     title = {Resolvent estimates for 2-dimensional perturbations of plane {Couette} flow},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2002},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2002__2002__a132/}
}
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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__a132/