Geodesic
On the problem of shear flow stability with respect to long-wave perturbations
Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 4, pp. 50-60 
S. V. Revina. On the problem of shear flow stability with respect to long-wave perturbations. Vladikavkazskij matematičeskij žurnal, Tome 18 (2016) no. 4, pp. 50-60. http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a5/
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     author = {S. V. Revina},
     title = {On the problem of shear flow stability with respect to long-wave perturbations},
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     url = {http://geodesic.mathdoc.fr/item/VMJ_2016_18_4_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

To find secondary flow branching to the steady flow it is necessary to consider linear spectral problem and linear adjoint problem. Long-wave asymptotics of linear adjoint problem in two-dimensional case is under consideration. We assume the periodicity with spatial variables when one of the periods tends to infinity. Recurrence formulas are obtained for the $k$th term of the velocity and pressure asymptotics. If the deviation of the velocity from its period-average value is an odd function of spatial variable, the velocity coefficients are odd for odd $k$ and even for even $k$. The relations between coefficients of linear adjoint problem and linear spectral problem are obtained.

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