Group Classification of the Unsteady Axisymmetric Boundary Layer Equation

Alexander V. Aksenov () and Anatoly A. Kozyrev
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Alexander V. Aksenov: Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, 1 Leninskie Gory, Main Building, 119991 Moscow, Russia
Anatoly A. Kozyrev: Dukhov All-Russia Research Institute of Automatics, Rosatom, 22 Suschevskaya St., 127055 Moscow, Russia

Mathematics, 2024, vol. 12, issue 7, 1-10

Abstract: Unsteady equations of flat and axisymmetric boundary layers are considered. For the unsteady axisymmetric boundary layer equation, the problem of group classification is solved. It is shown that the kernel of symmetry operators can be extended by no more than four-dimensional Lie algebra. The kernel of symmetry operators of the unsteady flat boundary layer equation is found and it is shown that it can be extended by no more than a five-dimensional Lie algebra. The non-existence of the unsteady analogue of the Stepanov–Mangler transformation is proved.

Keywords: symmetry operator; Lie algebra; group classification; axisymmetric boundary layer; Stepanov–Mangler transformation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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