Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

The Search of a Group of Transformations Admitted by the System of Equations Describing the Motion of Viscous Incompressible Conducting Fluid

Author(s):

S. Y. Malamanov

Faculty of Applied Mathematics - Control Processes,
doctoral student.
Saint Petersburg State University,
Saint-Petersburg, Russia.
Candidate of Physical and Mathematical Sciences.

stevmal@mail.ru

Abstract:

The paper deals with the problem on the searching a group of transformations admitted by the system of equations describing the motion of a viscous incompressible conducting fluid. We evaluate the system of differential equations connecting only the invariants of the subgroup of the main group of non-uniform stretching allowed by the system. Then we find the group of transformations admitted by the obtained quotient system.

Keywords

• : group of transformations
• differential equations
• invariant solution
• reducing the order

References:

1. Novozhilov V. V., Pavlovskiy V. A. Ustanovivshiyesya turbulentnyye techeniya neszhimaye-moy zhidkosti[ Steady turbulent flow of an incompressible fluid ]. SPb: SPbGU, 2013. 483 s
2. Ovsyannikov L. V. Gruppovoy analiz differentsial'nykh uravneniy [ Group analysis of differential equations ] M. : Nauka, 1978. 400 s

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