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Symmetry classification of Newtonian incompressible fluid’s equations flow in turbulent boundary layers. (English) Zbl 1516.35026

Summary: Lie group method is applicable to both linear and non-linear partial differential equations, which leads to find new solutions for partial differential equations. Lie symmetry group method is applied to study Newtonian incompressible fluid’s equations flow in turbulent boundary layers. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra such as Levi decomposition, radical subalgebra, solvability and simplicity of symmetries is given.

MSC:

35B06 Symmetries, invariants, etc. in context of PDEs
35Q35 PDEs in connection with fluid mechanics
76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics
17B66 Lie algebras of vector fields and related (super) algebras
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