Three-dimensional subalgebras of invariance algebra of Euler equations

Abstract:
We investigate the infinite-dimensional algebra A(E) of Lie invariance of the Euler equations which describe motion of an incompressible ideal fluid. An exhaustive list of A(E)-inequivalent three-dimensional subalgebras of the algebra A(E) is constructed. These subalgebras can be used for Lie reduction of the Euler equations to systems of ordinary differential equations or for finding partially invariant solutions and group invariant solutions without transversality.