Symmetry classification and invariance of the Reynolds equation

Abstract

In this essay, extensions to the results of Lie symmetry classification of Reynolds equation are proposed. The infinitesimal technique is used to derive symmetry groups of the Reynolds equation. Onedimensional optimal system is constructed for symmetry sub-algebras gained through Lie point symmetry. At the end, the general symmetry group of the non-conservative generalized thin-film equation are determined.