Geodesic
Nonlinear stability of a parabolic velocity profile in a plane periodic channel
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 11, pp. 1903-1922

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An inviscid or viscous incompressible flow with a general parabolic velocity profile in an infinite plane periodic channel with parallel walls that can move is considered with the impermeability conditions (for the Euler equations) or the no-slip conditions (for the Navier–Stokes equations). The nonlinear (for the original equations) and nonlocal (for all Reynolds numbers) stability of the unperturbed flow with respect to arbitrary two-dimensional smooth perturbations of the initial velocity field is established. 
@article{ZVMMF_2013_53_11_a11,
     author = {O. V. Troshkin},
     title = {Nonlinear stability of a parabolic velocity profile in a plane periodic channel},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1903--1922},
     publisher = {mathdoc},
     volume = {53},
     number = {11},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_11_a11/}
}
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O. V. Troshkin. Nonlinear stability of a parabolic velocity profile in a plane periodic channel. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 53 (2013) no. 11, pp. 1903-1922. http://geodesic.mathdoc.fr/item/ZVMMF_2013_53_11_a11/