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## Full classification of motions with uniform deformation on a rotating plane

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Rozanova O. S., Turtsynskiy M.

### In book

Vol. 2164. , AIP Publishing LLC, 2019

Rozanova O. S., Turtsynskiy M., , in: Nonlinear Analysis and Boundary Value Problems. Vol. 292.: Springer, 2019.. P. 131-143.

We show that a small correction due to centrifugal force usually neglected in the l-plane model of atmosphere drastically influences on the stability of vortices. Namely, in the presence of the Coriolis force only there exists a wide range of parameter ensuring nonlinear stability of a vortex with uniform deformation. Taking into account the centrifugal force ...

Added: October 31, 2021

Danilov V., Gaydukov R., Russian Journal of Mathematical Physics 2015 Vol. 22 No. 2 P. 161-173

A fluid flow along a plate with small irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure, i.e., both a thin boundary layer and the classical Prandtl boundary layer are present. It is proved that the solution of the boundary-value problem thus obtained exists and is unique ...

Added: September 3, 2015

IEEE, 2015

Added: March 16, 2015

Springer, 2015

This book gathers a selection of invited and contributed lectures from the European Conference on Numerical Mathematics and Advanced Applications (ENUMATH) held in Lausanne, Switzerland, August 26-30, 2013. It provides an overview of recent developments in numerical analysis, computational mathematics and applications from leading experts in the field. New results on finite element methods, multiscale ...

Added: October 10, 2014

Chernousova E., Feng Y., Hryniv O. et al., Mathematical Population Studies 2020

In a lattice population model where individuals evolve as subcritical branching random walks subject to external immigration, the cumulants are estimated and the existence of the steady state is proved. The resulting dynamics are Lyapunov stable in that their qualitative behavior does not change under suitable perturbations of the main parameters of the model. An ...

Added: October 28, 2020

Danilov V., Gaydukov R., Mathematical notes 2015 Vol. 98 No. 4 P. 561-571

We consider the problem of a viscous incompressible fluid flow along a flat plate with a small solitary perturbation (of hump, step, or corner type) for large Reynolds numbers. We obtain an asymptotic solution in which the boundary layer has a double-deck structure. ...

Added: September 27, 2015

Yablonskii S., Kurbatov N., Parfenyev V., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2017 Vol. 95 No. 1 P. 012707-1-012707-5

We study horizontal streaming excited by means of a low-frequency and low-intensity acoustic wave in 2D freely suspended films of thermotropic smectic liquid crystals. Acoustic pressure induces fast periodic transverse oscillations of the film, which produce in-plane stationary couples of vortices slowly rotating in opposite directions owing to hydrodynamic nonlinearity. The parameters of the vortices ...

Added: October 30, 2017

Myshkis P. A., Международный журнал по теоретической и прикладной математике, классической и небесной механике, космодинамике 2013 № 2(3) С. 51-59

In the work received the necessary and sufficient condition for the existence for linear differential equation of n-th order the fundamental system of solutions expanding in Taylor series on multiple degrees of argument in the neighborhood of zero. Such condition is that coefficients of the equation have analogous decomposition. In the proof used the transition ...

Added: February 18, 2014

Gaydukov R., Borisov D. I., Mathematical notes 2016 Vol. 99 No. 5 P. 636-642

A fluid flow along a semi-infinite plate with small periodic irregularities on the surface is considered for large Reynolds numbers. The boundary layer has a double-deck structure: a thin boundary layer (“lower deck”) and a classical Prandtl boundary layer (“upper deck”). The aim of this paper is to prove the existence and uniqueness of the ...

Added: May 18, 2016

Castillo M., Bonilla M., Loiseau J. et al., IFAC-PapersOnLine 2020 Vol. 53 No. 2 P. 6788-6793

This paper deals with the stabilization of a class of time-dependent linear autonomous systems with a switched structure. For this aim, the switched dynamic system is modeled by means of an implicit representation combined with a Linear-Quadratic (LQ) type control design. The proposed control design stabilizes the resulting system for all of the possible realizations ...

Added: October 30, 2021

Chernousova E., Feng Y., Hryniv O. et al., Mathematical Population Studies 2021 Vol. 28 No. 2 P. 63-80

In a lattice population model where individuals evolve as subcritical branching random walks subject to external immigration, the cumulants are estimated and the existence of the steady state is proved. The resulting dynamics are Lyapunov stable in that their qualitative behavior does not change under suitable perturbations of the main parameters of the model. An ...

Added: October 31, 2021

Burov A. A., Guerman A., Nikonov V., Acta Astronautica 2018 Vol. 146 P. 181-184

We consider a gravitating system with triangular mass distribution that can be used as approximation of gravitational field for small irregular celestial bodies. In such system, the locations of equilibrium points, that is, the points where the gravitational forces are balanced, are analyzed. The goal is to find the mass distribution which provides equilibrium in ...

Added: October 1, 2018