Institute of Mathematics of NAS of Ukraine,

3 Tereshchenkivs'ka Str.,

01601 Kyiv,

UKRAINE

E-mail: rop@imath.kiev.ua

**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.