Integral analysis of three-dimensional map of perturbations of the Poiseuille flow in a tube / *D. V. Georgievskii.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 4. P. 40-45
[Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 86-91].

The linearized problem on stability with respect to the three-dimensional
picture of perturbations imposed on a steady flow of Newtonian
viscous fluid in a pipe (the Poiseuille flow) is analyzed. The evolution
in time of individual harmonics of perturbations both by angle and
along axial direction is studied. A passage to quadratic functionals
constructed on squares of perturbation velocity components
modulus as well as derivatives with respect to the radius of these
components is performed. The upper estimate of the stability parameter
is obtained. It results the lower estimates of the critical Reynolds
numbers in the cases of axially symmetric perturbations and
two-dimensional (both axially symmetric and asymmetric)

*Key words*:
linearized problem on stability, perturbation, Newtonian fluid,
Poiseuille flow in a pipe, quadratic functional, axial symmetry,
sufficient estimate, Reynolds number, Squire theorem.